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REQ: Youtube.apk - xda-developers
There are a few ways to get YouTube working again in that thread. I had uninstalled YouTube when it started not working, and all I had to do to get it working after that was copy the Gingerbread YouTube .apk (from the linked thread) into the /system/app directory using Root Explorer (from the Marketplace). After a restart it was in the Extras menu.
I'm not sure if you can just run the .apk directly (my Nook kept refusing to run the .apk), but if you want to try that and you get an error that basically says you don't have permission to install, go into the NookColor Tools (under Extras) and uncheck then recheck the check box for "Allow Non-Market Apps". My Nook started allowing installs after that, but I had already fixed YouTube, so I'm not sure if installing it that way would fix your trouble--but it's free to try if you don't already own root explorer.
Also, I used the auto-nooter rooting method.