Looks like a pretty standard triangulation issue to me; as far as I know, Blender don't have a tool for manual retriangulation of invisible edges like for example 3DS Max so my guess is that the only way to avoid this is not to make heavily distorted polygons or to manually divide them into triangles.

After trying to re-state my whole point as clearly as possible for almost 2 hours, i somehow found/stumbled upon what u r trying to say by going to sculpt mode in wireframe view, and the tris can be seen across every quad. Holly molly!!

So, ultimately, every "anomaly" I mentioned, exist in other corners too, just that they were difficult to stumble upon when doing normal stuff (as they align with the direction of the grab, anyways, this detail's not important now).

When i was reading about different basics before starting into 3D thing, i had read somewhere that everything in 3d is ultimately made up of tris/triads. But seeing many tutorials, especially about topology, which emphasize hard core on quads, I almost forget that ultimately, binary is the foundation (ohh, and now i am using a stupid metaphor ??). So mano-wii (won't waste ur time by mentioning), yes, that is indeed intended, but at a quite deeper level than I observed.

So, i'm sorry for missing the crucial detail before reporting.

Technically it is possible to make polygons fill depending only on the view (without this triangular tessellation).
But that's not how things work today in the world of 3D computer graphics.

Edit: U already said it here:

In T67733#736114, @Alex (SpectreFirst) wrote:

the way to avoid this is to manually divide them into triangles.

so, this comment is of no use now, and i am removing the file.

~~~@Alex (SpectreFirst) I found a way on how to make it work. Just join the opposite vertices of the face (check the file:-). What this does, is it overrides the underlying invisible tris.
Here's the file explaining it (hopefully ?? !)
{F7630321}
Also, try switching between weight paint view and vertex paint view.~~~