YouTube for iOS has just received an update that has given the app a little bit of a redesign - following the update to Android.
This new app now allows you to multi-task, you can minimize a video into the corner while browsing the rest of the app. You can of course bring it back to full screen or you can swipe it away to get rid of it.
Another little addition is that you do all this and stream to your Chromecast, supported TVs or your PS3. When one of those devices is connected to your WiFi network, you'll see a new button in the top right that lets you push it to that device. It's perfect for something like the PS3 where you don't have to use the controller anymore to search for videos - the larger iPad screen is much better.