Cool, I'm going to go to the Apple store and go on a spending spree courtesy of OP! 😉
Seriously though, I don't think there's much to worry about. You can take the video down just to be safe. But no one's going to get any additional personal information from you about that.
People buy and sell iPods all the time on EBay. Everytime they do, they have the serial number of the previous owner (who probably registered the unit with Apple.)
Even if someone reported it stolen (unlikely since there's no benefit), you could easily show ID to prove you are the registered owner.
Just take down the Youtube video, and carry on as usual... 🙂