1) It doesn't work well with Opera. Until I upgraded, I couldn't even type in the login box. It's still buggy.
2) The annoying sound the inbuilt chat client makes for new messages always interrupts my music.
3) It's bloated in firefox. I really notice it on my slower computer
4) It's so much of a walled garden. Why can't I import photos from flickr, or export them?
5) Photo upload in general sucks. The java applet is fail. The fix? Yahoo already made it for you.
6) My events: I finally worked out where the export-to-google-calendar link was, and they are published without a timezone. So now, I'm busy going to places at 3am.
7) You call it an API, but it's not an API to access data and remix it.
8) Where's my xmpp compatible chat, eh?
Basically, it irritates me that the developers they have working for them don't care about these things in the slightest.
Worse, it's sucking up and doing poorly all of the functionality I had in external services. My 2nd tier friends seem to use facebook chat over MSN or Google Talk.
On the other hand, LuckyCal almost promises to be useful.