For me the biggest annoyance is music discovery (as mentioned above). Its UI seems designed to hide, not suggest, new treasures in the library. Not sure if it bugs everyone equally (I went with Beats - am I the only one here? - over Spotify for the same reason), but while I can dig for titles I already know, not sure the suggested playlists and albums are enough to find new stuff.** I want to cut them slack as they're new... in the US. They've had time to sort out before arriving here, no?
For instance Tidal open screen (mobile):
Halloween Creepy, Pumpkin Party Dance, Tidal Tuesday, and First Listen SXSW 2015 playlists
Four albums covers shown without titles & descriptions (I can guess the artist for one)
Versus Beats open screen (mobile):
Bjork Influences playlist, Nilsson's Aerial Pandemonium Ballet album, Ali Farka Toure self-titled album, Orchestras for Blue Moods playlist, Sonny Rollins' Way Out West album, Guest List: Sonic Youth playlist, PJ Harvey's To Bring You My Love album, Shirley Horn's Close Enough For Love album, Van Morrison's Saint Dominic's Preview album, etc.
**If I was coming straight from MOG, which wasn't updated for some time, I suspect this would bother me less.