In the beginning of the movie, Handsome Harry shoots a hole in his hat to give the kid a scare. He comments that it is his only hat. In the rest of the movie, that same hat does not have a hole in it.
When Bess and Harry are playing poker in the hotel room, Bess is holding 6 cards in her hand, not 5. Then she puts her cards down and says, "Full house!"
When Bess is performing Shakespeare for Harry, she indicates that the scene is from "Macbeth". It's actually from "The Winter's Tale".