(at around 12 mins) When Leo's ex wife comes to visit him before The Purge begins, she looks over at a selection of newspaper articles and photos of his target stuck to the wall. After she leaves, he also looks over at the wall, but the layout of the montage has changed dramatically, including completely different photos.
(at around 1h 9 mins) When the group goes to Tanya's house, the door is locked, and Tanya opens it. After they leave her apartment, Sergeant Leo Barnes goes outside to check on the situation, and comes back through the door, unlocked. The next scene involves the team using a saw to cut the bolt on the door.
(at around 15 mins) Just prior to when the car breaks down they are driving under the bridge, ground level, when it breaks down they are on top of the bridge.
(at around 1h 30 mins) At the end of the movie Eva places her fingers on the chin of Cali while talking to her. The take ends with Eva swiftly taking her fingers away. The subsequent take starts with Eva's fingers on the chin, hereafter she removes her fingers once again.
(at around 1h 35 mins) The movie is set in 2023, at the end of the movie it states there is 364 days to the next annual purge, 2024 is a leap year, making it 365 days till the next annual purge if held on March 21st at 7.00pm.
(at around 15 mins) Shane and Liz's car breaks down after being tampered with. While looking under the car there is fluid dripping and cut wires hanging. This however does not make sense. Shane says he lost power steering , car stalls, and cranks but doesn't start. If an electrical circuit is cut that keeps the car from starting, they couldn't have left the market. This "tampering" would have been much better explained by a broken drive belt, with a cut mark halfway through it.
The film takes place in Los Angeles on March 21-22, 2023. The Purge begins in total darkness at 7pm and ends in daylight at 7am. Unless the Founding Fathers abolished or changed Daylight Saving Time, the opposite would be true.
(at around 1h 2 mins) The news crawl on the TV (at the party Eva takes the group to) has some mistakes, such as learning from "other's" mistakes (instead of "others'") and spelling "Parliament" as "Parliment". The crawl changes when someone walks by, too, suggesting a hidden edit.
(at around 19 mins) Sergeant Leo Barnes listens to the radio in his car, a 2011-2014 Dodge Charger. He shuts off the radio by pushing the "Screen Off" button. In reality this would shut off the screen only but leave the radio playing.
Barnes' car is clearly armored to a high extent, as it suffers numerous direct hits from what is clearly a very high power weapon and emerges unscathed. At the same time, the car is shown accelerating very quickly from a standing position, making extremely sharp turn at high speeds etc. No car armored to that level could possibly handle like that. Characters are also shown opening and shutting the doors to the car as if they were normal doors: armored doors would be extremely heavy.