Ooh, the scolding! If my sim-kids are 5 minutes late for school, they get yelled at, and by the time all is said and done, they're at least an hour late for school. That doesn't make sense. . .
And the cooking, with everyone trying to make their own food instead of eating from the food put out. I make liberal use of the 'Call to Meal' command to get around that one. I also have one sim bring another drinks/glasses of nectar, so they don't make their own. Or I have a family member act as a bartender, which seems to stop other sims from making their own drinks.
I've actually never played an Over-Emotional sim, so I can't speak to that one, but the idle animations can really get on my nerves.
Babies. Either they're ignored, or they're swarmed by every adult in the house, and they all proceed to take the stinky toddler, and give it a bottle, when I'd much rather put the kid in the high-chair! And putting it back in the crib? Questionable at best.
And the entire household (plus guests) will be obsessed by something, right now it's the Gnubb set, previous examples include the Water Slide and the Hot Tub.
I almost never switch families, so Story Progression isn't that much of a problem for me. I usually play legacy-style, even if I'm not playing a legacy.