The Apple YouTube app only showed you videos that would play. The desktop version of the YouTube shows you everything, including videos that will not play on the iPad (or in some cases any mobile device).
Besides the apps that Kevin mentioned, you can also visit the mobile version of YouTube at m.youtube.com . This site will only show you what can be played. Most of the time this is what I use. It's not a bad interface, but most serious YouTubers seem to prefer the apps.