I think for Live Chess on the iPhone/iPad, you should be able to see the existing challenges that are being sought, and to pick from there. The ability to challenge/accept games on that platform is too limited.
T/B and Live Chess app suggestions
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Also with the iPad/iPhone app I would definitely like to see the possibility to make premoves, sometimes ther are just "only" moves and it feels dummy just to wait to make that same move anyway. An option to email games would be a nice feature, as well as live observing of titled player games. For turn-based games I would definitely need the ability to make notes for myself (in that iPad app).
I have a couple of suggestions for both turn-based and live chess on the iPhone app:
For Live Chess, there should be the option of emailing the game to yourself for study, like on turn based games.
For Turn-Based games, there should be a way of offering a rematch challenge to someone you just played. I will often times finish a great game with someone that wants to play again but we are both playing on phones and cannot start a new match until the next time we are at a computer. You can rematch right away in Live Chess, I would think this would be simple!
If there are in fact ways for this to be done and I just don't see it, let me know!