Vintage Synth Repair

Hello, all.  I'm new to the group.

I just got a Moog Prodigy of Ebay that looks like it's been sitting in
a garage for 20 years.  It plays, but it needs work, and I plan on
replacing some parts.  Primarily, I'm trying to figure out how to tune
it.  Specifically, the keys are not in tune with each other.  That is
to say, if I play a scale, the low C and high C are a half step apart!
(and octave + half step)  When playing melodies, it sounds terrible
because some notes are ok and others are flat/sharp.  Just wondering
if anyone had any suggestions/knowledge on what would control
individual note/key pitch, and how I can repair/correct this problem. 

On a side note, which components on a Prodigy (or any Moog synth,
really) tend to fail or falter over time?  My point is, I'm wondering
where to start, as far as replacing components goes, that I may see
improvement in overall sound quality and playability/reliability.

Thanks!

Dustin