The painted-on "HMS Bounty" on the Bird-of-Prey is visible only when Kirk asks his crew if they will stand trial with him.
Right after the Bounty has landed in the park and the trash men start to flee, some of the trash cans nearest the truck are full to or nearly to the tops. But as the truck drives off, those cans appear to be empty.
The boat shown in the movie is too small to be used in whaling. It is a fishing trawler with a harpoon attached.
The hand that Kirk uses switches when he melts the lock during the rescue of Chekov from the OR.
Scotty was promoted to captain sometime before the events of Search For Spock and retained that rank through his appearance in The Next Generation but he is inexplicably wearing commander rank in the final scene where he stands with the crew to answer the charges against them.
Ships in the opening sequence that are affected by the probe lose power and come to an almost complete stop. In the vacuum of space, air friction does not exist, so they should keep going the same speed they were before.
When the whales are beamed into the tank, it appears to be completely full of water; no air space is shown. The whales would eventually drown.
The military would not have turned Chekov over to the police. If for any reason they would have to have a special doctor, they would have brought the doctor to the patient.
When the Bird of Prey is seem warping towards the Sun, the Sun is shown to glow with a pale yellow light, but in space, it would glow with a bright white light, since the Sun only appears yellow from Earth's perspective due to the atmosphere.scattering blue light.
When Kirk asks Scotty how long the transporter bay is, he replies, "About 60 feet." Other units of measure throughout the movies have characters using metric units (meters, kilometers, etc) so it seems much more likely that Scotty would have said, "About 18 meters."
The Bounty's bridge looks very different than it did in Star Trek III: The Search for Spock (1984). It's possible that the Vulcan engineers working on the ship renovated it.
When Spock nerve pinches the punk on the bus, his music appears to stop even though no one actually turns it off. However, it can be presumed that the punk's head hits the 'off' switch.
When Sulu plots a course to pick up the whales, Admiral Kirk orders full impulse power. Sulu states an ETA of 12 minutes. From San Francisco to the Bering Sea is about 2825 miles. Full impulse power is listed as 1/4 the speed of light, or approximately 167 million MPH. With these figures, the trip should take about 0.06 seconds, not 12 minutes. It has been established in the Star Trek canon that impulse drive is not usually used in atmosphere, thrusters being used instead.
The whalers speak Finnish, but they are in the Bering Sea, part of the north Pacific Ocean. As Finland has not commercially hunted whales in well over a century, the Finns may be mercenaries for Japan, which was still involved in commercial whaling in 1986.
When Spock is being tested by the computer, some camera angles are shot through the display screens. The text when viewed from the back is still displayed forward, which can be explained as a feature of a holographic alien device from the future rather than a goof.
When the cloaked ship lands on the grass, a trash can is crushed. As the earth (grass) moves down under the pressure of the heavy ship, the grass blades remain pointing up.
During landing of the ship, garbage cans are "blown over" into the prevailing wind, and can be seen being kicked over by garbage man.
When Gillian is touching the cloaked ship at the park, there is a shot from above that reveals her right foot steps under the matted shot of the ship's print on the grass.
When Kirk takes Gillian's arm to take her toward the back of the ship to the whale tanks, he walks her directly into the door jamb. She hits it, recovers, and continues.
When the elderly lady is being pushed in a wheelchair, happily saying, "The doctor gave me a pill and I grew a new kidney", the nurse on the left side of the screen almost trips over the wheelchair, but manages to recover.
There's no way the whales could have been transported from San Francisco to the Bering Sea in a few hours. Plus the whales would have been relocated to warmer waters. Also the 'Norwegian whaling ship' would operate in waters such as the Norwegian, Barents & Greenland Seas and the northern Atlantic Ocean and not the Bering Sea.
The characters criticize the brutality and short-sightedness of man in killing off humpback whales but completely disregard the brutality of the alien race that is about to kill off millions of species on earth over the absence of the whales.
While on Vulcan, the Klingon vessel is being serviced by Vulcan engineer wearing red pointy hats, but their Vulcan ears seem to be too big, and don't match the skin tone of the Vulcans.
Dr Taylor is driving Kirk and Spock back to the Park where the ship is cloaked. Before they reach an actual Street they travel through a very long parking lot parallel to the water. Through this parking lot they pass a number of vehicles and trash cans perpendicular to the route of travel. They are not seeing exiting onto a street with two-way traffic.
The Macintosh that Scotty is using to come up with the formula for transparent aluminum would have to have been loaded with very complex software to come up with the formula. Computers of this era would not have this capability and the Macintosh would have to churn for hours, having multiple discs inserted and removed. The discs which would have the capability of producing this very complex formula would not have been at Plastic Corp. Also Scotty's keystrokes were all over the place and on a Macintosh he also would have had to have been typing & swapping discs (had they been available) for hours.
The antique eye glass frames that Kirk sells to the antiques dealer when they first arrive in San Francisco are described as 18th century, but the frames have plastic temple tips and bridge pieces.
(at around 1h 2 mins) When Dr. McCoy and Scott are in Plexicorp, can be seen Scott using a 1986-vintage Macintosh Plus in order to create a 3D model of the transparent aluminum's formula. It would be impossible for any people of the year 2286 to use appropriately any 1986's technology (it means, three centuries ago) unless he was a special preparation for it. An example would be in a teenager of 2020 habituated to cell phones, tablets and touch screens trying to work with a 1990 IBM computer.
Star Trek IV- The Voyage Home officially takes place in 2286... and 1986. Star Trek II- The Wrath Of Khan began on March 22nd, 2285 (Stardate 8130.3), Admiral Kirk's 52nd birthday. The events between the beginning of the Enterprise's training cruise on the 23rd of March to the Enterprise returning to Space Dock after her battle with the USS Reliant, the detonation of the Genesis device and the birth of a new planet where the Matara nebula used to be, Spock's death and funeral, the transfer of Savik and David Marcus to the USS Grisom and the rescue of the Reliant's crew members left on Ceti Alpha V was roughly one or two weeks. Another several days went by between when Kirk learned that McCoy was holding Spock's Katra at the expense of his mental health, stealing the Enterprise (Stardate 8210.3) to return to Genesis and the fal-tor-pan ritual on Vulcan to transfer Spock's Katra back into his newly resurrected body. When Kirk, McCoy, Scotty, Uhura, Chekov and Sulu have agreed to return to Earth on the newly christened "HMS Bounty" to face court-martial, they have been exiled on Vulcan for three months. It should still be 2285.
When Scotty is typing on the computer in the plexiglass factory and his hands are shown, the sound effects of typing do not match up with his hands, which are moving much slower. In addition, there is no way a single keystroke as demonstrated by Scotty could create the level of graphics shown on the 1986-vintage Macintosh computer used in the scene.
When Spock tells Gillian that Gracie is pregnant, she brakes the truck and we hear a squealing sound indicating that the tires have locked-up and are skidding on the road. However, the scene immediately cuts to a side shot of the truck stopping and the wheels are not locked - the truck comes to a gentle stop.
When Sulu accidentally turns on the windshield wipers of the helicopter, the wipers were broken so a grip had to move the wipers manually. Look closely and you can see his finger holding on to the blade as it moves back and forth.
Just before Spock checks the bus map at a stop, you can see several crew members are visible through a large glass window of a restaurant - one of them even clearly wears a "Star Trek IV" security badge, and all are wearing walkie-talkies.
When Kirk and Spock are riding the Muni bus, a crewmember with a camera is reflected in the window behind them.
As Admiral Kirk answers Gillian's jab about not using money in the future and the waiter is handing off the check, someone can be heard laughing - perhaps at Kirk's joke.
When the tour group is viewing the whales from above and it it sprays water from it's blow hole there is a small amount of smoke (you can tell the difference from water spray by the way it drifts out) that trails out after the initial spray possibly from the charge used to propel the water from the prop whale blow hole.
Kirk and Spock are seen walking as Dr. Taylor drives up. She asks where they are going, Kirk replies "Back to San Francisco." The scene is shot in the Marina District of San Francisco. Kirk and Spock are already in San Francisco, Sausalito is on the other side of the Golden Gate Bridge which is behind them. While it is possible that Kirk may simply made a mistake being from the future, Dr. Taylor later even mocks him at dinner saying that they couldn't even get back to San Francisco without a lift.
When Kirk and the crew first exit the ship after landing in Golden Gate Park, Uhura says the whales are on a heading of 283 degrees (Spock repeats this heading at the bus stop). 283 degrees from Golden Gate Park heads straight out to sea without passing near Sausalito.
First glimpse of the Alameda Enterprise landscape.
After they all escape, Chekov's phaser is still in the possession of the military agents that had originally arrested him. While McCoy earlier in the film airs his concern to Scotty about leaving advanced technology (Plexiglas scene) or information of same in the past, no concern is given to Chekov's phaser, which is left behind. But then again it didn't work so it might be difficult to reverse engineer.
During the Klingon Ambassador's argument before the Federation President, he shows footage of the destruction of the Enterprise, including footage from inside the bridge. There is no way he should have possession of either set of footage. If the Klingon Bird of Prey somehow recorded the destruction of the Enterprise, there is still the fact that the Bird of Prey is in Kirk's possession. Any footage aboard the Enterprise would have been destroyed with it.
Chekov runs through an open door from the room where he's being questioned by the government officials. That door would certainly be closed when questioning an intruder with unknown devices on a Navy ship.
Error in temporal physics, possibly inherent to the time travel sub-genre of fiction: Even if it were possible to "go into" the past of 1986, the world of Kirk and Spock and the Enterprise would have automatically not existed, and therefore, even the smallest changes they made at the Institute and their dealings with others would have created a different time-line, even if they could precisely calculate when and how to "return" to "their time," their world and everything else in the galaxy would have been completely different. It is impossible to go back in time without altering the future that follows it. Even worse, McCoy goes about flagrantly altering history by growing the old woman a new kidney, which would lead to her having years of life which could not exist in the "original" time line. Also, the Bounty's arrival squashed a trash can which thus could not continue to be used for sanitation as it would in an unaltered time line. The novelization actually explains away the paradoxes by directly stating that many of the supposed changes were actually caused by them. I.e., they had to go back in time so that the timeline would be correct.
Kirk takes the attitude that he has no choice but to take Gillian with him back to the 23rd century. He has a transporter at his disposal and could deposit her anywhere on Earth instead of ripping her from her own time.
After the President gives his warning, Kirk gets up to talk to Spock.
In the tour group when Kirk and Spock first see the whales, there is a 20th century US Naval officer who doesn't remove his cap during the entire tour, even downstairs at the viewing area. Uncovering when indoors is such a basic uniform wear regulation that a first-week recruit at boot camp does it instinctively; a commissioned officer in public certainly wouldn't forget to do it.
When McCoy tries to discuss the afterlife with Spock, Spock states that they can't because there is no point of reference. McCoy then complains, "So I have to die in order to discuss death?" - McCoy DID, in fact, die, and then get "repaired" by alien technology in Shore Leave (1966), which both characters should remember.
Scotty asks Dr Nichols how thick a 10 foot by 60 foot sheet of plexiglass would have to be to withstand the pressure of 18,000 cubic feet of water. The pressure from water is determined by its "head", or depth, not by the volume. As an engineer Scotty should be aware of this.
Dr. Taylor gestures toward some orca sculptures while making a comment about whales. Despite the "killer whale" misnomer, orcas are not whales, but rather a type of dolphin. As an expert, she would know that.
Scotty is giving all measurements in English units, but Starfleet uses metric.