Continuity mistake: In the final scene, Kevin approaches the pigeon woman. She says "Merry Christmas" without any pigeons on her head. The long shot is taken, and she now has at least four pigeons are sitting on her head. A close-up is taken when Kevin approaches and reaches her hand, and again, pigeons have disappeared from her head. Impossible to have the pigeons flying on and off her head in the space of half a second.
Continuity mistake: Kevin is being served ice cream in his hotel room. A wide shot of the bed shows the food around it and the waiter scooping ice cream into a bowl. Look at the tall pink rose at the end of the bed, which towers out of its vase. In a couple of shots later, the rose suddenly becomes barely higher than the vase itself.