P3-24 pitch instability

That problem is why the table was sold. I would just buy a new motor. Bite the bullet and get a new motor.. It is the only way you will get rid of the problem.
(you SHOULD have tried to return the item to the seller, but it may be too late now.)
From viewing the video, That pulley is clearly messed up, and it will probably be the motor is too. I bet the pulley was screwed up, so a 'dealer', or the 'owner' bent it 'good enough', bending the motor shaft in the process. The owner did not get it resolved, and sold his problem to you.
(that is one of the joys of eBay, and one of the reasons I would NEVER buy anything on eBay, anymore: eBay is geared to support only the seller, Amazon supports the buyer, and I hope the goN' is fair to both.)
PS: no dealer is stupid enough to fix your table without a proof of warranty, and if they would, they are already out of business.. because if they are that stupid, they couldn't STAY in business.

Sorry to say, but now that we know you bought it used, I tend to agree with the others that it was probably sold because of the problem you're having, and that the motor needs to be replaced. Maybe the seller will split it with you. The good news is, a new motor is only around $100.

Well, if it comes down to it, I'm going to demand my money back via PayPal--it hasn't even been two weeks.

Ugh, this is annoying. There's actually another video I can share with you all.

This time, it's the spindle that's wobbling

http://www.youtube.com/watch?v=MekQTIxXnpY

The spindle is too much. Get your money back.

i recently bought a new rega p5 that had a very noisy motor, a sub platter that was totally wobbling, and the headshell was way off from being level. the table was a mess. i have had rega turntables for almost 20 years, but will never buy another.