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Just loaded up the Assasins vs Parkour video (in HD) and it streamed just fine though it did stutter a couple times. Never buffered. I just downloaded YT (guess my ROM didn't include it). Have you just updated the app?
I've been assuming the the Youtube app is just broken. Unfortunately there's no alternative on the Nexus 7 (I side-loaded Flash, but even Firefox - the only browser still doing flash - takes you to the Youtube app when you press on a video).
That's because you set it to. Go to Application Settings and tap Clear Defaults for the YouTube app. Next time it will ask you what app you want to use: don't tap Always if you'd rather it didn't do the same thing every time.
YouTube had been basically unplayable on both my HTC rezound and my N7. Doesn't matter if I'm on 4g or cable Wi-Fi, it plays for a second then ten minutes of buffering. I think the app is broke, haven't tried it on my computer.
What I did was uninstall the update and its been working much better for me on both my N7 on wifi and my GS3 through LTE.