Google have updated the iOS version of the YouTube app. Version 2.3.0 now has the iOS 7 style keyboard, improved layouts of the captions and subtitles and searching of videos, playlists and channels is brought together into one search result which should make it easier to find what you want.
You will find the app in the iTunes Store.
What’s New in Version 2.3.0
* Find videos, playlists and channels together in search results
* Formatting, positioning and user settings for captions / subtitles
* iOS 7 keyboard and other improvements