The PS3 has always sucked when it has come to viewing Youtube videos. They’ve hardly been viewable in the web browser with horrible quality. However, a while back a dedicated Youtube app was finally released. In order to install it on your PS3, go to TV/Video Services -> My Channels -> Youtube. Works great.
What’s even better is that in the latest update for the iOS Youtube app that came out today, they’ve added support for pairing your iPhone to your PlayStation 3 which allows you to search for videos on your phone and then show it on your TV via your PS3. I don’t know how long I’ve been waiting for this. It’s extremely convenient. And, yes, you can watch the videos in HD.