Continuity mistake: After Jack is blown out of the sky and is lying in the graveyard, he has several grey smudges on his face from the explosion. But in the very next shot, a birds-eye view of Jack lying across the angel, the smudges have disappeared.
Continuity mistake: When Jack is having his Santa joyride, the army is called in to shoot him down. There is one sweeping shot of the giant cannons rising and firing at him. If you look at the bottom of the screen, you can see two small soldiers as the guns are rising, but as they fire, the soldiers blink out of existence.
Continuity mistake: When Sally delivers her care package for Jack, he is writing on his chalkboard. He scratches his head with the chalk in his hand. As he pulls his hand away, the chalk disappears mid-shot.