Corrected entry: Towards the end of the movie Tony Lip shoots off a gun in a parking lot of the Orange Bar to scare off would-be criminals who were hiding just behind their car. (When this happens Dr. Don Shirley shouts out, "I knew you had a gun Tony", which makes the theater audience laugh). But if Tony would have had a gun on his person for the entire time, the police would have found it when Tony and Don were taken to jail in an earlier scene.
Corrected entry: Tony is told by Dr. Shirley to pay for the jade stone, but it shows him shoving it back into the wooden box at the outside of the store, so he doesn't have it any more at that point. But in the ending snowstorm it reappears.
Corrected entry: Don Shirley asks Viggo Mortensen who is singing a certain song on the radio. He replies something to the effect that it's Aretha Franklin, and that she's really something. But it is highly unlikely that Aretha had sufficient (or any) airplay, popularity or name recognition in 1962 to make this scene credible. Columbia Records had her under contract and did not do a particularly good job with her. It wasn't until 1967, after she signed with Atlantic Records, that she became known much at all and her career really took off.