YouTube on iPad stopped playing (error playback)
Have you tried to restart the iPad yet: press and hold both the Power button and the Home buttons together for at least 10 seconds, until the Apple logo appears, then wait a bit, then check.
If that does not work, please uninstall the Youtube app:
Then go to App Store on the iPad, search for Youtube, download it, and check.
Also, if needed, please disconnect the power cord from your internet/wireless modem/router device for a couple of minutes, then reconnect and check.