Seeing the pics corroborates my earlier 1986 model appraisal, though it has been updated with a circa 1988 Chorus rear derailleur with the adjustable parallelogram angle, an adjustable stem, new saddle and ATB pedals. I've never seen a fender routed over the brake caliper! I think that may top the stem.

Regarding the slipping gears, the tension screw on the levers, as suggested by oddjob2, if the first thing I'd look at. A misaligned hanger, as suggested in the previous post is another possibility. It could also be stiff chain link, worn or sticking freewheel pawls, or a combination of new chain with an old freewheel (or vice versa). The worst scenario would be a cracked frame which can excessive flex and resultant ghost shifting.