The biggest pet peeves of mine when it comes to games localization is the fact that they left out the important plot points or change up the characterization of that one character.
Splatoon for example, In Splatoon 2, Mr. Grizz in the localized English version and the original Japanese version are very different characters. It was not until Splatoon 3 that Mr. Grizz was more in line with the Japanese version due to the plot importance in the hero mode (Alterna). Octo Expansion in the localized English version left out the reason why Commander Tartar wanted to wipe out the current species (to create a perfect species or species that resemble humanity, but feel free to correct me on that).
Fire Emblem is one of the biggest examples of this, with FE: Fates being dubbed one of the "worst localizations" in Fire Emblem games.