It is indeed possible to have crisp polypaints, but not if you haven’t been given a polypainted tool.
You seem to be having some confusion over the distinction between displaying a texture and displaying a polypaint, so I’m not quite sure what you’re doing because your description is a little confusing.
Poly painting is stored inside your ztool, and it’s detail is not based on image resolution but rather on the subdivisions of your model. You can observe this by going to a low detail level of your polypainted model, you’ll see it get blurry, because each polygon is only one color, or a gradient (there is a switch in the poly painting pallette). So millions of polys = high detail. That’s why uv’s are irrelevant to your polypaint.
A texture is, of course, an image file, which is displayed on your model via uv coordinates.
It’s important to understand that textures in zbrush override poly painting. So if you have the “texture on” highlighted in the texture pallette you can’t see your polypainting (but its still there).
The point of all of this is that if you were handed off a file with no polypainting assciated with it, with uv’s and a texture file, and if that texture is too low res (zbrush can export 1 2 3 and 4k images), then when you convert that texture back to a polypaint it will faithfully, and with very high quality reproduce the pixelated look of your texture. It can’t invent detail that doesn’t exist. So you might be screwed. But if you still have the original polypaint you can just make a new texture.
You just need to figure out what you’re looking at. Go to the texture rollout and make sure “texture on” is off. Then go to the polypaint rollout and click “colorized” on and off. The model will switch between your blank material and your polypaint. If that polypaint is pixelated then that’s all you’ve got and you’ll just have to redo it or live with it.
Also… Just wanted to mention that the “the residue squares” you were seeing, though everything feat said was true, could also be an area where you inadvertently painted a different material onto your model. Note the distinction between painting with rgb highlighted and with mrgb highlighted. Just thought it might be that because you can’t see part of an old texture, if texture is on, then that’s what you’re seeing. Though bad uv’s could make it display improperly.
The videos on the pixologic website under education help for a lot of this stuff to understand how zbrush functions, because its very different from other apps and at first is incredibly frustrating.
Hope that helps…