I've been playing "MediEvil", lately, and it got me wondering: what causes some of the old 3D games to have "flowing" graphics, when moving? It's present in games like "Final Fantasy VII", "MediEvil", and I remember "Dungeon Keeper 2" having the same thing in zoom mode. However, examples like "Quake 2" didn't have this "issue", and it's just as old. The resolution doesn't seem to be the problem, everything is rendered perfectly fine when you stand still. Is the game refreshing slowly, or is it something to do with buffering?
I have only the most bizarre of citations for this, but it appears on the original PlayStation, the vector unit (which was usually used to transform vertices) was capable of fixed-point operations, and the rasterizer also used fixed-point math, but only integers could be passed between the two. So you're seeing quantization artifacts: polygon corners are getting snapped to the nearest grid point. Perfectly stable for a still scene, but fairly disconcerting in motion.
From a little bit of additional research, it appears that the original PlayStation had different resolutions at which the rasterizer could work, from 256x224 to 740x480. So you could pick lower resolutions to get better fill rate, but you'd see these sorts of artifacts, as the grid at low resolutions is coarse enough to easily detect with the naked eye.
If you play Quake 2 in software mode, it actually does have some of the issues you mention. If you look at certian models at sharp angles in Quake 2, you'll see "swimming" textures. This is because many early 3D engines used affine texture mapping. This saves you the expensive per-pixel divide that gives you perspective correct texture mapping, but it means your textures will warp when viewed at sharp angles.
Also, many early 3D games (including Quake 2) used simple vertex morphing to animate their models as opposed to skeletal animation. The vertices are tweened between keyframes with linear interpolation. Naturally, this doesn't preserve the distances between vertices very well, so you end up with jelly vertex syndrome—the models jiggle a little bit as they animate!