Factual error: A toy modern four-door automobile and a clear plastic ball can be seen as the children play when the Burgermeister comes in on his wheelchair. Both unlikely for a story set (presumably) in the 1800's, at the latest.
Continuity mistake: When Edgar takes Duchess and the kittens to be abandoned in the countryside, he is on a motorcycle and sidecar combination. During the trip, the sidecar changes from one side of the bike to the other and back again. Also, when the sidecar separates from the motorcycle while the dogs are chasing Edgar, the wheel on the sidecar switches sides regularly as well.
Revealing mistake: The wires holding up Jacob Marley's floating lock box and chains are visible. (00:32:10)
Continuity mistake: In one scene when Hudson and Andrews enter the vestibule of her house, Rock can clearly be seen to have "mutton chop" sideburns. However, once inside the house, they're gone. When he goes back outside, they're back.
Revealing mistake: Whenever Stupid Bat is flying, the wires pulling him up are visible.