Continuity mistake: In the scene where Ava shoots Damien, she has no bra under her sheer nightgown in one shot and then has one when she goes to the window in the next.
Plot hole: Towards the end of the "The Hard Goodbye" segment from the first film after Marv has killed Cardinal Roark, a newspaper clipping shows that the Cardinal's brother Senator Roark was decrying the atrocity. However, at the very end of this movie, Nancy kills Senator Roark with Marv's assistance. Since Marv was captured and imprisoned immediately after he killed Cardinal Roark, that means that the killing of Senator Roark had to have occurred before "The Hard Goodbye", which means Senator Roark should not have been alive to decry his own brother's murder.
Continuity mistake: When Dwight is taking pictures of Joey (Ray Liotta) and his mistress, she takes her top off and gets on the bed, and hands him the handcuffs. He takes the cuffs and immediately cuffs her, and has sex with her. When they are done having sex, she is now wearing something, but she is still cuffed. No way she could have got dressed or even reached her clothes while still being cuffed.
Factual error: When Joseph Gordon-Levitt is playing poker, they are using Morgan style silver dollars. The stacks of dollars are treated as $100 dollars. But a Morgan dollar is 2.4 mm thick, a hundred dollars would be 9 .44 inches high and the stacks of coins were about half of that. (00:11:00 - 00:12:00)