Continuity mistake: The tiger bites the seat off the suitor's trousers, allowing the viewer to see his polka-heart boxers. When we see the tiger in the courtyard, he has a part of the same boxer shorts in his mouth. So if he bit off the seat of the trousers, shouldn't he have purple cloth in his mouth? (00:11:45)
Factual error: The baby is expanded to approximately fifty times his height, width and girth but it's explicitly stated that he retains his orginal mass. This means he will have the same volume as one hundred and twenty five thousand babies of his original size, but will weigh the same as before he was enlarged! That child is going to weigh much less than the volume of air he displaces. He's going to float away.
Revealing mistake: When Rizzo falls down the chimney and lands on the goose at Bob Cratchit's house, he burns his feet. When he is next to Gonzo, his feet are smoking. If you look closely, you can see the holes in the puppet's feet where the smoke comes out.
Factual error: The old man is supposed to have accidentally ended up at Rita and Peter's wedding by just "getting on a train," and finding himself in Lake Forest (a far northern suburb of Chicago.) But he started out in Berwyn (a western suburb), and in order to get to Lake Forest from Berwyn, you have to get on one train, get off in downtown Chicago, walk several blocks, and then get on an entirely different line going to Lake Forest. In other words, not something you can "accidentally" find yourself doing, but something you have to know where you are going in order to do.
Continuity mistake: When Chet and Stanley asks Irene some questions (in the café, about 15 minutes into the movie) about the murder, the cigarette Irene smokes changes a few times between the shots. Most obvious is the length of the ashes. (00:16:13)