I'm having the same issue. When I search for it in the market, it says "Open" as though it's installed, but when I click open, it brings me to the install screen. I hit install, it shows the progress bar for a second or two and then goes away. I can see Youtube in the manage apps screen, but not in the app drawer. If anybody has any suggestions here please let me know.
If it's just a select few of us, then maybe I'll try a factory reset. I'd just hate to lose all the setup work I did on it today.