Problems with the Classic Client bars off the top of my head:
1. Sometimes the health bars stop updating correctly, this happens with both regular bars and party bars but I'm not sure what the cause is - maybe too many bars at the same time? (note: I've never had this to my own character's bar, only bars for other players and NPCs)
2. When someone joins a party, all the open bars jump to a new position.
3. When someone disconnects and then reconnects, all the open bars jump to a new position.
4. Party bars have no background - this can at times make the bars a little hard to see if they are over the game window and not the blackened area (on principle, they should have backgrounds)
5. Sometimes a bar will only become dark gray when a monster dies rather than disappear like it should.
6. This is a minor gripe, but it annoys me that bars locked together will all close when one is right clicked. This is annoying because if you want to close just one you have to alt+click to separate it first.