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It is a know issue. Direct from Google:
We are currently working on an update for the Android YouTube app v2.1.6 to resolve this issue.
As a temporary workaround, some users have found that rebooting the phone (turning it off, taking out the battery, reinserting and turning the phone back on) fixes this problem and videos begin playing normally again. Or, you can also use our mobile website (m.youtube.com) until the update is released. Thanks for your patience.