(at around 4 mins) When Jim puts the puppy, Lady, in her basket, he puts down some paper on the floor. A few shots later, the paper disappears.
(at around 1h 7 mins) When Lady enters the baby's room while Tramp is fighting the rat, the chain is gone. When Lady goes to the fallen crib when the baby's crying, the chain is back on. Then when Tramp comes over to her as Aunt Sarah enters the room, the chain is gone again. And then the chain is back on lady as Aunt Sarah grabs Lady and pulls her down to the cellar.
Tramp's color changes from brown/tan to dark-gray/gray. In his first appearance at the rail yard, he is clearly a brown dog with tan belly. By the end of the movie, he is a dark gray dog with a gray underbelly. He switches back and forth a couple of times during the film.
(at around 35 mins) After ''The Siamese Cat Song'', when Lady is chasing the two cats, the cats knock down blueish colored curtains which tangle up Lady. After Aunt Sarah comes into the room, the curtains are red.
(at around 34 mins) As the Siamese cats are pulling on the mantle to get at the fishbowl, in one shot the pattern on the mantle does not advance as it is being pulled.
(at around 25 mins) The calendar showing the passage of time are inconsistent in their dates from one month to the next. First, December 31 and then January 1 are both Thursdays. Next, November 30 is depicted as a Friday, while December 1 is a Tuesday. Finally, both January 31 and February 1 are a Sunday.
(at around 5 mins) The shadow under the door extends too far. The light source would have to be on the floor to cast a long shadow.
The opening of the movie takes place at Christmas, as evidenced by the snow outside, but the kitchen calendar says "April".
(at around 54 mins) At the beginning of the dog pound scene, during the first verses "No Place Like Home", the shadows of the bars on the dogs distinctly resemble the stripes that were usually shown on prisoners, a comic effect that makes the pound seem like prison. But in the last verse, those stripes are gone. This was possibly intentional, as the joke could be assumed to have made its point by then, and the shadows would be too distracting during the following dialog.
When the Siamese cats let the tablecloth pulling the fish bowl go, it makes the sound of breaking glass, but in the next shot, the bowl is still in one piece.
The film is set in 1910, but the Siamese cats appear completely modern. The modern Siamese cat, with its elongated snout, slender bodily structure and triangle-shaped head, did not develop until the early 1950s. Prior to this time, all Siamese cats were rounder and had a less exaggerated appearance.
(at around 9 mins) Serving coffee and doughnuts to your dog is not the wisest thing to do. While the doughnuts are simply lacking in nutrition, coffee is outright toxic to dogs.
(at around 21 mins) Swatting your dog for misbehavior usually just confuses or frightens the animal, as happens with Lady when Darling strikes her. This one is a case of Values Dissonance, because corporal punishment (for both dogs and human children) was perfectly acceptable at the time of the film's release (and especially in the time period of the film).
(at around 40 mins) The beaver exclaims, "Listen, listen sonny, you realize every second, seventy centimeters of water is wasted over that spillway?" Water is supposed to be measured in volume, not length, so it would be more technically accurate to have used "cubic centimeters" in place of "centimeters". However, for very casual estimates, the Beaver may have meant that the stream moved seventy centimeters downstream each second, regardless of the depth at any point, or the width of the hole being plugged.
Leaving a muzzle on a dog for longer than 30 minutes can be extremely dangerous, especially if it keeps the dog from fully opening its jaws.