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.
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)