normally I can find any solution with google but I'm hitting dead ends.
I just jailbroke my iphone 4 4.2.1 with Greenpois0n and now my youtube app doesn't work. Just a black screen. Also, any embedded youtube videos in apps just show the gray graphic with the play button crossed out.
I'm assuming you have an official SIM that you used to activate, so I don't believe it is a hacktivation issue. I'm thinking you might need a restore and rejailbreak. I've used GP on many iPhone 4's and no YouTube problems on any. So it could just be a jb gone wrong.
Just in case anyone finds this thread and is having the same problem, it happened again. I dug a little deeper and found that hiding the native YouTube app thru SBSettings caused the embedded youtube files in all the apps to quit working.