When the waiter gives Don the check at Harry & Joe's and he reaches for it, the glass, ashtray, napkin, and cigarette all change position between camera shots.
Don removes from his typewriter the title page for his novel "The Bottle" and crumples it up. Near the end of the movie, Helen hands it to him as a flat, crisp piece of paper.
Don Birnam stops at the "A. Bloom" pawn shop. When it is closed, he walks uptown. He passes another pawn shop with a man standing in front of it, and the name "A. Bloom" is again seen.
Toward the end of the movie, Don's coat is tossed to the floor. A few shots later, it's lying on the arm of the chair.
While at Nat's Bar, in medium shots, Don's glass is a small, smooth shot glass. In closeups, however, it is a larger, jigger-sized glass with faceted sides.
On Saturday Don goes in search of a pawnshop. At the second pawnshop called "A. Bloom" (see Continuity), a man informs Don that the shop is closed on the Jewish holiday of Yom Kippur (Day of Atonement). This could not be true, as the modern Hebrew calendar in place since the 12th century CE is designed so that Yom Kippur cannot take place on the Sabbath.
When Don is in Nat's bar drinking shots of rye, the number of shots is depicted by the increasing number of wet rings left on the bar each time the shot glass was refilled. Several rings collect on the bar, each remaining as wet as the last. In actuality, the glasses would leave rings only if the alcohol had been cold, which would have caused condensation of atmospheric water vapor on the outside of the glasses. Since the alcohol was at room temperature (the bottles were sitting out in the bar when the bartender poured from them), there wouldn't have been any condensation, therefore no wet rings would have been left on the bar.
At one point in Nat's, Don Birnam grasps and shakes the bar vigorously. In a real saloon, the bar would be so heavy and solidly attached to the floor that a person could not do such a thing.
When Helen pours whiskey for Don, then divides it into two glasses, it is nowhere near a quarter of the way up the glass. When Don chooses not to drink it moments later and drops his cigarette in the glass, it is more than half-way full.
When Don and Helen's parents are sitting back-to-back in the hotel lobby and he's listening to them, the shadow/light on his face changes sides between the front and back camera shots.
While drinking at the bar Don's glass leaves water rings on the counter. After a while there are 12 rings. But the water of these rings do not evaporate, as if they were all made in fairly short order. Instead, some of the rings should have just been a dried residue and others in various states of evaporation.
The flashback sequence takes place in 1934-1935 (as per the poster outside the Opera House), but all of all of the women's hair styles and clothing are contemporary with the making of the film, and they remain so as the story moves ahead to 1937.
(at around 10 mins) As Helen and Wick are descending the stairs, a shadow of the boom microphone can be seen moving through the sunlight on the wall behind them.