Continuity mistake: When Buddy and Walter are on the landing of the stairwell at the police station, the view looking down on the duo shows Walter close to the wall and window, while the view of Walter's back shows both of them closer to the stairs and further from the window.
Deliberate mistake: In the orphanage scene, Santa's bag drops dead center in the fireplace. The noise of the impact gets baby Buddy's attention in a quick shot, and the camera shifts back to the fireplace. Now, the bag has shifted to the viewer's left when Santa's boots are coming down. The shift of the bag is presumably to make room for the boots coming down the chimney.
Continuity mistake: When Jovie kisses Buddy at the skating rink, her left hand is wrapped around Buddy's neck. The next shot of Jovie finishing her kiss has her hand in a different position.
Continuity mistake: When Walter is apologizing to Buddy in Central Park, the view over Walter's right shoulder shows he and Buddy looking at each other almost at eye-level. However, the scenes over Buddy's left shoulder shows him towering over Walter and Walter is also looking up at Buddy.
Continuity mistake: In the meeting scene with Miles Finch, Walter is speaking to Buddy. Behind Walter, Finch's right hand is resting on the edge of the table. The next shot shows Finch's same hand resting on his notebook.
Visible crew/equipment: Widescreen only. When Buddy is chasing down Michael after school, just before the camera cuts if you look at the far left of the screen you can just see a boom mic entering the shot.
Continuity mistake: After baby Buddy crawls out of Santa's bag at the North Pole workshop, he is partially sitting on the edge of the bag, grasping the leg of a teddy bear. The next shot and the baby is over a foot from the bag, and not holding on to the bear's leg, which is still in the bag.
Continuity mistake: Buddy's left arm moves to support Baby Susie under her feet, but the next shot shows his left hand between Susie and his chest.
Revealing mistake: When Buddy confronts the Department Santa (Artie Lange), watch the kid sitting on his lap. He's mouthing the words both Buddy and Santa are saying.
Visible crew/equipment: When Buddy fudges with the fake Santa and the mall is destroyed you get a glimpse of the lighting set up and a crew member in the top left of the screen.
Revealing mistake: When Buddy is first seen walking toward Gimbels, the man in the costume is Will Ferrell's stand-in. His hair extends below the hat.
Plot hole: Throughout the film we see several characters talk about how there's no Christmas spirit and how nobody believes in Santa anymore. If, in this universe at least, Santa does exist, it's almost impossible for people to think this. If the parents deliver the presents then how do they explain the excess gifts that Santa brings? We know that Michael is on the nice list because Santa shows him towards the end, so Michael must get presents from Santa. There is no way that Walter can't believe in Santa then because Michael gets gifts from him every year.
Suggested correction: Emily and Walter probably just thought each present Michael got from Santa was from the other parent. I'm not sure if Walter got him presents or not but you can see that Emily did as she's seen walking home with presents when she's on the phone with Walter.
That is highly unlikely. When my daughter was "believing in Santa" age, my wife and I always talked about what we were getting her, so we didn't duplicate. Plus that theory wouldn't work for single parents.
It is very likely because it's obvious Walter is not in the Christmas spirit like his wife and Michael are. Plus it's obvious Walter is not focused on his family at the beginning of the movie so it's safe to assume the original submission is correct.
Other mistake: How was Buddy able to buy the negligee for his father? He has no money.
Continuity mistake: In the snowball fight scene we see some snowballs hit the rock behind them. The snow on the rocks keeps disappearing and reappearing between shots.
Other mistake: When Buddy confronts the department store Santa (Artie Lange), watch the kid sitting on his lap. He's mouthing the words of both Buddy and Santa as they're saying them.
Continuity mistake: When Buddy is in the Lincoln tunnel, the busses alongside him change positions between clips.
Other mistake: When Buddy's brother gets a skateboard from Santa Claus in Central Park the skateboard trucks are mounted incorrectly. Both are mounted the same direction. The kingpin always faces the inside of the board, but here one is mounted facing outside.
Continuity mistake: When Buddy is drinking the Coke, the bottle turns to show the label.