Continuity mistake: Just after the beginning, the Aussie man, walking with a tiny dog, has an ice cream in his hand that vanishes - one second it's there and the next second it's gone.
Other mistake: When Mickey gets shot there is a close-up of the pistol. The empty shell casings coming out in slow motion are from blank rounds.
Continuity mistake: In the restaurant scene, Jackie and Mickey are having a discussion. The latter drinks martinis and then steals the former's beer. In one shot, Mickey's drinking deeply from the beer glass, and then puts it down, but in the next shot, there are only martini glasses on the restaurant table.
Suggested correction: Starts w/ 2 full beers, M sucks "that beer" down as if there's only 1. Waiter comes back with 3rd martini, M asks if he brought J a beer, but there's still a full glass on table. After waiter leaves there are 2 full beers on table again! Then Mickey's drinking a half glass of beer! Waitress brings another martini, right after that there's half glass of beer and empty martini glass! Then back to full glass of beer and another half glass and 2 martinis, 1 half full. Then back to 1 beer/1 martini, etc.
Continuity mistake: When they are drinking martinis and beer, he is about to drink the martini and the glass is full - he starts talking about why he might be going to jail for a shotgun. As he is talking they cut away to Brad Pitt and then back and the glass is empty sitting on the table. They cut back to Brad Pitt as he is still talking and then back again and the glass is full as he is taking a sip.