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.
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.
Continuity mistake: When the Winter Warlock's icy heart melts, he is holding a toy locomotive with its front showing, but the next shot shows the locomotive's rear showing.
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.