Here's something I find annoying: Pokémon with a useless Ability. I'm not thinking about Abilities that are always useless, such as Defeatist or Slow Start. I'm thinking about Abilities that are useless for a specific Pokémon, which also happens to have the Ability in question. Everyone knows about Rotom-Fan, the Flying-type with Levitate. Sadly, it isn't the only one.
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Upon its introduction in Gen 5, Stunfisk had Static and Limber as its regular Abilities, as well as Sand Veil as its Hidden Ability. Not the best Abilities in the world, but all three of them had a basic function at least.
In Gen 6, things changed. Stunfisk still had the same Abilities as before, but now, one of them had become useless. Starting in Gen 6, Electric-types are immune to Paralysis. Thus, Stunfisk having Limber became pointless since it would already be immune to Paralysis as it is an Electric-type. While it can still make use of Limber if it changes type, such as through Soak, Reflect Type or Camouflage (RIP), that is extremely situational. Stunfisk is essentially stuck with one of its Abilities being completely useless. That said, the situation for Stunfisk isn't as bad as it is for Rotom-Fan. Stunfisk has two other Abilities that it can have, and those do something at least, while Rotom-Fan is forever stuck with Levitate. Still a bit of a shame though.