I'm always agonizing over this, since I dislike most of the miscellaneous small cards that aren't part of decks.
The most annoying thing about the expansions is that usually when they add new encounters, they can't resist referring to lots of tiny little extra cards, which means I have to have a huge stack of miscellaenous tat beside the board.
Dunwich Horror - has some Arkham Encounters which make you flip over the 'special condition' cards. (In my experience, the conditions are almost completely pointless. Darke's Blessing and the Coded Messages are the two which are potentially useful, but they're not so great that it's worth intentionally trying to get them activated.) And regarding the Other Worlds: like with Kingsport, there's always an 'Other' option on the encounters, but that tends to homogenize the OWs a bit, so I always cut the cards that refer to worlds that aren't on the board.
Curse of the Dark Pharaoh has numerous encounters which require the 'Barred From Neighbourhood' cards - surely the most pointless small cards ever. It also has several encounters (in Arkham and Other Worlds) which give you Benefits and Detriments. The good Benefits aren't good enough, the bad Detriments aren't bad enough, and none of them are common or game-changing enough to make up for the faff of putting the cards beside the board in the first place. So I usually cut any encounters which refer to those cards, mainly out of protest at the inelegance of the design...
King in Yellow has the spells whcih create 'Magical Effects'. These aren't so bad, although it's a mystery to me why the full effect wasn't just crammed on to the spell card itself.
Black Goat of the Woods - there are about ten Arkham encounters whcih give you a Cult membership, scattered across three or four unstable locations. Even if you're only using the encounters from the base game and Black Goat, the chance of ever getting a Cult membership are slim, and it's not like a Cult membership is particularly good anyway. If you use all the Black Goat Arkham encounters, you need to use Cult memberships, which means you need to use the Cult Encounters deck, which means you need to use the Corruption cards. And the only way to make any of this absurd appartus DO anything is to use the Black Goat herald itself, in which case you don't need the Arkham encounters since everyone will be swamped with Corruptions anyway (and Corruptions are the interesting part).
Mostly, it seems like AOs were probably meant to be 'expansion-generic', i.e. you can usually use them with just the base game and they'll still work. Investigators are a bit more particular, though: the Librarian, Musician, Martial Artist, Soldier and Bounty Hunter all have fixed cards from their respective expansions.
The Sailor is (I think) the only investigator who makes specific reference to an expansion component in a special ability, and although it doesn't require you to use Innsmouth, the investigator is strongly targeted at playing with boards which have more aquatic locations.