Chess.com app - no. 1?
Nevermind the big masters (thinking themselves big people) telling hus how they prefer ICC or Playchess. Chess.com got the best iPhone app. ICC's ok, Playchess.com's just horrible. Chess.com got the cleanest and most user-friendly interface, with more functions.
One of the main reasons I signed up for Chess.com is all the excellent video lessons they got. I love how easy it is to watch them, while riding the train, on your phone. Thumbs up for that!
I think they should allow you to view the opening explorer and to watch your game archive via the app though. Hopefully that will come.
Also, right now the video library is chaotic on the iPhone. You can only view the videos according to date. If you find a video lesson you like that's divided into multiple parts, you'll have to remember the name of the video, type it into the search box and then hope you find the previous or next part. When you view a serialized video lesson you should be able to view links to the other parts as well!
Other than that, kudos!