This has been on ongoing problem for most, if not all Android phones have while sometimes trying to play YouTube videos. I doubt that the problem is your device, I believe this problem is cause by either the Adobe flash player, or the length of time the video takes to buffer. Either way Google need to address this issue. Most times tapping on the thumbnail video does seem to start playing the video.
*Note*
You could uninstall and reinstall the "YouTube" app, or uninstall and reinstall the adobe flash player updates. Menu - settings - applications - manage applications - downloads. And for the YouTube app... go to All.
I hope this work out for you.