Any ideas on what would make it skip
so easily?

Could be simply that it was a POS. Hows are the isolation mounts?

POS?... maybe in terms of long term reliability, but there is no way
they could have sold these if they were this bad when new.

The isolation mounts seem OK. Spring and rubber bushing are intact at
each suspension point.
Could it be that the rubber bushings are hardened from age and ned to
be replaced?

We had similar problems in our 97 buick, although not as bad. No
problems the first few years, but as the car got older, the CD got more
sensitive to bumps in the road.

WRT electronic skip protection mentioned by other posters, I also doubt
that this radio had it, but it did not used to be this sensitive to
bumps. Something in the CD played has degraded mechanically or
electronically.

Paul