Most likely a weak laser due to the age of the unit, an alignment could possibly help, as mentioned above. I had an ol' Luxman with the exact same problems which I sold to someone who was able to fix it -- by replacing the laser. You may be better off looking for a new or more modern used unit.
Sometimes skips, sometimes doesn't
I have an ancient ('85) dbx DX3 CD player that I stubbornly nurse along. The dbx dynamic processing board (DAC?) in this ol' girl simply blows away anything else I've heard. Its only problem is its proclivity to occasionally suffer skipping episode; sometimes a few blips, sometimes a hard, sticking stutter. Cleaning the disk helps, even if it's already clean. Often, wiping just the outer edge seems to clear the problem. I can put the skipping disk in my Sony DVD player and it'll play just fine (though not sound as good). Some evenings, its a frequent problem, but at other times, it'll go days without a skip on the same disks that made it stutter before. What I find odd is that old disks with visible surface scuffs have no effect on playability or skipping. I just had the unit cleaned and aligned by a good shop, which improved the skipping situation considerably, but it's still an annoying problem. Is there something more to skipping than disk surface cleanliness?