Anime

I would also like anime to be as faithful as possible, but there are examples of anime with translations that are intentionally maliciously changed. Miss Kobayashi's Dragon Maid being the low hanging fruit here with the infamous "patriarchy" line. People are finding more distasteful changes in other anime localized by Jamie Marchi (and others).

If you mean an example of something like a joke that may not translate properly, puns are commonly the cause of necessitating such changes. But in the case of a joke regarding specific geography, I cannot think of one, but I mention something so specific because there may be a show that has it, and in that case IMO the context of the scene should be taken into consideration, as well as the original author's intent. If the author wants someone to laugh there, then it would be on the localizer to make sure that scene is funny in the target language. If the joke goes over the heads of its viewers because its something they couldn't understand I would say its important to defer to the author's intent of that scene being funny, while ensuring the potential replacement is as analogous or similar in the target language as possible. So a similar joke that is more generic or understandable would be better IMO than a direct 1:1 translation. Of course, this is an edge case and not common, but still a potential.

If i was on my pc atm i could pull up an article with way to many examples, but one off the top of my head is a recent remake of a romcom has a localizer literally saying the show sucked and they fixed it. Can't think of the name atm. I know a boys love manga called I Think I Turned my Childhood Friend Into A Girl (or something like that) turned a character trans, kinda ruining the point of yaoi. Mushoku tensei apparently got a lot of censorship.

Here's an article of bad English localizations in games and anime, https://nichegamer.com/8-years-awful-localizations-games-anime