One thing that infuriates me is when I don't get shown a Tweet from an account I follow, only to be notified that someone else 'liked' the tweet. Just show me the Tweet! I follow the account because I want to be kept up to date with it. Not be kept up to date with it when someone else I follow likes it!
I'm very lucky I can just leave Twitter for days/weeks on end. I know for some it's become a necessity.