Paulie sees the woman enter the PIN code 5070 into the ATM, but he uses a different code to withdraw money with her stolen card.
In various different scenes, Paulie's wings are seen to be clipped. Any scenes where he isn't flying, his primary feathers have been clipped, you can see when he opens his wings out. Later in the film they say they are clipping his primary feathers but up until then, he is supposed to have had unclipped wings.
When Paulie first uses the ATM machine for money, he puts the card in. In the next shot when he's flying away, the card isn't in the slot anymore.
When Marie and her mother are hugging each other after Marie says, "Cup" while struggling, you can see that Paulie pooped on the table.
When driving to Los Angeles with Ivy, Paulie says that the largest desert is at the north pole when in fact the largest desert is Antarctica which is at the south pole.