Continuity mistake: Ann visits her mother's grave at the cemetery with her father, who wipes off snow from the mother's photo on the marble. Couple of minutes later, a new shot shows the photo covered in snow again.
Plot hole: After Ann retrieves Tibor Zoldan's music box from the pawn shop, she finds the incriminating photos of her Nazi father, Michael Laszlo, hidden in it. Even though Zoldan (who had died) could have redeemed the music box from the pawn shop within a certain time period, it makes no sense that he would have pawned it with the photos left inside. The photos were how Zoldan was able to blackmail Laszlo. It's highly unlikely he would have forgotten they were in there.
Continuity mistake: When Ann leaves the hospital after questioning the elderly man, she is carrying a purse. When she gets out of the cab to walk along the river, the purse has disappeared,.