mesh faces not real polys

If one takes a four verticie polygon lying flat on an x - y plane and move one verticie in the z direction, it is no longer a real face. If you look at it one way, it appears to be a four pointed polygon, but at another it appears as if it were made of two triangles.

How do you treat this kind of mesh form when you are modeling?
Is it good practice to eliminate them, or does it not matter and you disregard them? What are the cons and are there any pros to this kind of paradoxical form? In what situations are they clearly undesirable and what situations is it too much trouble to correct them?

In general, you ignore it, unless it affects the rendering of your model. Most of the time, you don’t have an isolated four vertex plane, the quads will be part of some larger mesh, and this effect won’t be noticable.

In the cases where it does affect the render, you can force the render to be how you want it by splitting the quad into two triangles, and arranging the triangles the way you want them.

You can’t really eliminate them. Blender uses quads as a modeling basis, and does not define how the quad is split into triangles, leaving that up to the renderer. The only time it is ever a problem is in extremely low poly work, such as using a single cube for an entire building, and then, for some reason, tweaking a corner so it is out of square.