Continuity mistake: When Kevin is running away from Harry and Marv he buys strings of pearl necklaces, and pulls them apart on an icy corner. When the bandits slip on them, there are more pearls there than Kevin dropped.
Continuity mistake: In the scene where Harry and Marv are at the skating rink, the front of Marv's hair is constantly changing from shot to shot. It's either poofy or pulled back due to the earmuffs he's wearing.
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.