If anyone can help me with this question, I'd greatly appreciate it.  I'm new to all of this.

 Here's my story.  I had a Realistic turntable for years.  It worked okay, but on a whim I purchased a new LP in a record store because it came with a MP3 download of the album, and I really don't need any more cds.  Anyway, I had a great time listening to it on my old turntable and began searching around for an upgrade.  I came across a Beogram RX2 on E-Bay and went for it.  It set me back $60.  So, it arrived yesterday in wonderful condition and packaged nicely.  The seller had the disclaimer that it "started up and would stop".  I knew it was a risk to buy it, so I was pleased when I loaded my new LP on the platter, turned it on, and it started playing.

Here's where the story gets interesting (at least for me).  It seems as if there's some friction that causes the record to spin unevenly, thus producing an uneven sound and the tones warble.  Now, this new LP is one of those new "high quality 180 gram records".  Before deciding that I'd wasted my $60, I went and pulled out an old album of my dad's from the 70's, put it on, and it sounds great.  With the old record, there's no friction noise while it spins, and it plays beautifully, producing a much better sound than the old Realistic.

Does anyone out there have any experience with this or thoughts on the matter? 

I've no knowledge of the RX2 but it sounds suspiciously like a worn/loose belt to me (assuming it's belt driven of course).

Very nice radial deck, the RX2. Have undone the transit screws completely? Is the platter level or is it a it low? The leaf springs may have sunk a little but you can adjust these. Also check that the platter is centred. It is a belt drive deck and this may need replacing as Puncher suggests.

The service manual is available on site if you were to upgrade to silver or gold membership

I'm puzzled that it would play one record beautifully and another very poorly.  Again, I have no experience in this area, so I very much appreciate the feedback.