Yeah it happens to many devices.
It happened to my Palm Pre a lot.
Sometimes it'll play... other times not. Some videos cannot even be played by the Youtube app.
In this case find the video on your browser. Remember, if you're on Froyo... you have flash. (Best to turn flash settings to on demand, so you can click on the video to activate flash when you want it).
Then when it is playing, tap and hold on the video. You'll see a fullscreen icon top left of the video. Click on it.
That's the best thing you can do besides watching it from the Youtube App.
Hope it helps.