I haven’t had an iPhone for a long time but from what I’ve remembered the YouTube app wasn’t that great at all. With iOS 6 they’ve pulled it and you now have to download the YouTube app from the app store. But before you do, you should check out another app called Jasmine. It’s a pretty nice YouTube client. It’s got a nice clean layout and it’s very simple to use.
You should also check out some of Vihart’s videos they are pretty mind blowing!