Continuity mistake: Shortly after Jasper & Horace steal the puppies, a blue Renault 4 is seen going past the entrance to the mews. About 3 seconds later it goes past again in the same direction.
Continuity mistake: When the puppies are watching the television, you can see that they are watching Homeward Bound. The three animals are standing on the hill, about to head home. A few minutes later, when the nanny comes inside, we see the TV again and Shadow is with Peter. This happens at least 10 minutes after the animals are on the hill.