When talking to Chili and Evie, Steven Tyler says that he has never appeared in a movie up to this point and doesn't want to start now, obviously a sarcastic line as he is in the film. However, he forgot Wayne's World 2.
Chili Palmer lists stories in which the narrators are dead mentioning Casino as one example. However, although Casino gives the impression that the narrator is dead in the opening scene (the car exploding), we later find out he in fact survived the explosion.
The Aerosmith tattoo on Edie's back when she is outside on the lawn chair and Chili first sees her in the movie is obviously different than the one she shows Steven Tyler later in the movie at the Lakers game.
When Sin's gang hangs Raji off the balcony, his hat is gray. As the hat falls and the camera follows it down, it's brown. Then, when it lands on the cement and the Russians pick it up, it's gray again.
At the end during Linda Moon's performance when Elliot is waving to Chili and Edie, you see the break dancers starting to dance behind him; when he is exiting the stage, you see the same dancers just getting on stage.
Towards the beginning of the movie when Chili Palmer and Tommy Athens are at the sidewalk coffee shop, there are two women sitting at the table directly behind Chili Palmer. In one shot, the woman closest to Chili Palmer cuts her food with her fork and brings her fork to her mouth to eat, but there is nothing on her fork.
When the Russian confronts Chili after killing Tommy, we see his right eye is black. However, later when the receptionist is explaining what happened when the Russian visits Tommy before killing him, Tommy is seen swinging his right fist at the Russian. This would have blackened the Russian's left eye.