Oh boy, the list is long. I'd add my thoughts and say that I don't like
The generic preset Miis who ALWAYS gives you the adventure quests while the Miis in your save data are stuck with the errand quests.
The delivery cats
Any traveller from the Travellers' Hub who want a vacation, it must be the most common type of random quest
Kind Miis who are only known for sparing monsters (Their other two quirks can be learned by anyone of any personality at a high enough relationship level)
The sickness mechanic
That one Mii who always buys HP Bananas and MP Sweets instead of weapons and clothing
I'm surprised no one mentioned Twerkies and Terror Fiends yet.