I have attached two sample images to illustrate the problem I'm having. The game tends to lose track of what some of the textures (tiles?) are supposed to be. This can affect walls or doors or buttons or even lasers. The samples I've attached come from "L.A. Rumble", but the issue occurs in all episodes. I'm hoping someone will recognize the distinctive patterning of the glitch and tell me if it can be fixed.
There are two temporary fixes I know of. I can save the game and begin again. The other fix, oddly enough, is to dive underwater and resurface! I do find that coming into contact with water, or turning on night vision, tends to cause the problem more readily, but sometimes it happens for no reason I can fathom.
I'm running Windows XP SP3 on a Hewlett Packard Pavillion A1410Y, which has an ATI Radeon Xpress 200 card (driver version 8.593.100.0, dated October 2, 2010). I am not using any fancy EDuke stuff like HRP or Polymer. If it matters, my resolution is 1440 x 900.

It seems I've found the solution!
After playing 80% of the game I was getting irritated by the display glitch. So I tried this, that and the other thing. And the thing after that. And so on.
Eventually I appeared that my HP Pavillion A1410Y's video card (ATI Radeon XPress 200) was being affected by the Catalyst AI setting, which was helpfully enabled by Radeon's Catalyst utility. Disabling this feature made the graphic issue go away.
Apparently, Catalyst AI is a set of optimization routines that are intended to make the video card faster and better. In this particular instance, however, it caused problems.