The YouTube app on the iPhone has not received an update since it was originally released. The mobile version of YouTube instead is more feature rich compared to the app. And if you don't want your iPhone always opening up the app but instead watching a video on the mobile page then Mac OS X Hints has a simple way of stopping that from happening.

You can go to Settings > General > Restrictions. Flip the YouTube slider to off. The YouTube icon will disappear and you can load up a video in the browser with no app required.

[Mac OS X Hints]