(at around 7 mins) While Scamp is chained to the doghouse at the beginning of the movie, the length of the chain changes significantly throughout the scene.
(at around 58 mins) After Tramp fights the big dog inside the dog pound the door is shown open behind him as the fireworks are going off, but as the dog catcher returns there is a sound of the door opening and the dog catcher is shown pushing the door even though it was already fully open.
(at around 56 mins) When the dog catcher carries Scamp into the dog pound there is a barrel on the doorway's left, but when he leaves and slams the door it switches to the right side, only to switch back to the left side again when he returns after the dog fight.
(at around 9 mins) After Scamp first sees the junk yard dogs and the dog catcher, the broken barrel by the gate vanishes after the dog catcher drives away.
The movie takes place seven months after Lady and the Tramp (1955). Scamp and his sisters should be adults at 6 months but they remain as puppies. Lady was 6 months when she turned into an adult in the first film.
(at around 21 mins) In the "Junkyard Society" song, one of Sparky's lines are "No distemper shots from the vet". The distemper vaccine did not exist in 1911.
A stray Dobermann (or mix, as Buster is a bit stocky for a Dobermann) in the Edwardian Era, especially in America, is unusual considering it was a new breed dating back only a few years.
The film is set in New England, but the dogcatcher has a Southern (perhaps North Carolinian) accent.