Continuity mistake: When Cratchett gets the bird from the shop, it's clear that the bird is a duck. But throughout the entire film he's referred to as a goose.
Factual error: At the early stages of the movie, Scrooge is talking to a man who owes him money. Scrooge mentions the August Bank Holiday. Bank holidays were not introduced until 1871, after the period in which A Christmas Carol/Scrooge is set - around 1835 (Charles Dickens, the author of the book, died in 1870).
Factual error: When Scrooge is in the carriage with his girlfriend in the back, on the hill you can see a white van go past.