Aunt Sarah, especially to people who aren't dog lovers. It's possible she's just prejudiced against dogs and doesn't like them. It's also possible she didn't want to allow any animals near the baby, since she did leave her cats downstairs (although she brings them upstairs with her after their Wounded Gazelle Gambit). Though many would still call it an overreaction to see a small family dog wag its tail and angrily chase it out of the room as if it was a rodent.
The alligator in the zoo. Trying to eat Lady or trying to help remove the muzzle - and simply not realising his mouth was too big.
The rat gets this too, to a much lesser extent. Was it truly trying to kill the baby, or was it only focused on using the house as a shelter? Though if you pay attention in its fight with Tramp, the rat at some point prepares to jump into the baby's crib.
Anvilicious: Only irresponsible troublemakers dream of a life that doesn't involve staying where you are, raising a family and doing what your owner tells you.
The dog catcher is perhaps the least evil of the Big Bad Ensemble; his job is to find dogs and put them in his pound to await pickup, but the film generally portrays him as antagonistic for this, particularly when he agrees to have Tramp put to sleep.
Though she may be particularly harsh towards Lady and the Tramp, Aunt Sarah does what she does out of concern for others, particularly for her cats (who get Lady muzzled with a Wounded Gazelle Gambit) and for Darling's child. Plus, she hates runaways (and also, it would seem, strays), to the point of chaining Lady to the backyard doghouse to teach her a lesson, and around the time she arranges for Tramp's euthanasia, she's only aware of two things as far as the surrounding circumstances were concerned: one, that the child's life was in danger, and two, that two dogs, one of them a stray, were at the scene.
Fair for Its Day: Luigi and Joe's Italian stereotypes are far more cartoonishly exaggerated than Si and Am's, but haven't seen quite as many complaints because they're arguably the nicest characters in the movie, especially since they go out of their way to make a date for two dogs as romantic as possible.
Family-Unfriendly Aesop: Aunt Sarah insisting only cats should be left with babies. Leave it to Lady to prove she can. Now here's some real-talk: If you pay any remote attention to the news, one should be careful about leaving a baby or young child unattended around a pet. Doesn't matter how well trained you think they are, or if they're not a dangerous breed, animals can get jealous of the attention the newborn gets (or, just as dangerous, misguidedly treat the infant as one of their own young) and, intentionally or not, hurt them. Cats can suffocate a baby unintentionally by laying on them, and dogs might just attack them out of the blue even if the dog normally acts gentle, or try and pick it up like it's a toy or its own baby.
Narm: When the rat is bitten by Tramp the first time, it squeaks like a chew toy. (It squeaks normally every other time, not even close to narmy.)
Woolseyism: When Lady is upset about Jim Dear having referred to her as "that dog", the word they use in the Norwegian dub is more of a slang word for dog ("bikkja") making her shock even more understandable.