graphical glitches with overlapping polygons

I just cycled through the rendering modes in the editor viewport. It’s weird… Both “Unlit” and “Lighting Only” have NO visible overlaps/glitches/artifacts, but the other modes do. Don’t know what to make of that.

Here’s a picture of the (prototype) material I am using:

I guess I could also try to get some pictures of the actual glitch itself. I just don’t know, if it’s easy to see without motion.