Normally using a full frame lens on a DX camera means you are cropping the outer part of the image - the place where the most distortion occurs. There are some types of distortion that show up in the center of the frame - or at least around the center. Since the DX crop is rendered larger for the same size print, I guess you could argue that visible distortion or lens issues are magnified on DX. But in my mind, that is a bit of a stretch.
Probably a bigger issue with an older wide lens like the 20mm is that new designs generally have provided a lot of improvement. Wide lenses tend to have a good bit of distortion, and newer designs have gone a long way to eliminate or reduce those problems. Wide lenses are also subject to flare and other problems. The coatings on newer lenses provide a lot of improvement to older lenses in difficult shooting conditions. And almost all new lenses are better optically than older lenses.
Here's a good article from Thom Hogan on lens kits. It contains some of the older lenses, as well as links ot other reviews. Thom tends to have a pretty good perspective. http://www.bythom.com/rationallenses.htm
And Here's a link to lens reviews by Bjorn Rorslett. He's also a pretty good point of reference. You'll note that he provides feedback on some lenses for multiple cameras - and the performance can vary. http://www.naturfotograf.com/index2.html