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All 3D objects, whether they are used in an animation or in rendering a static scene, are subject to non-planar errors if they use polygons with more than 3 sides. It's worse in animation, because the vertices are moving, and part of the polygon can suddenly flip to facing the other way, disappear completely, or not display its texture properly.
The problem is simple: if you create a square, then move one of its points perpendicular to the other 3 a little distance (or a lot), the square is non-planar. Or move the point so that any of the outside angles is acute (less than 90 degrees). Now you're in even worse trouble, because 3D programs have no definition for how to render this object. By definition, a triangle cannot be non-planar, because whenever you move one of the points, the whole surface tilts accordingly.
Most (if not all) rendering engines automatically convert all polygons into triangles anyway. If you do it yourself, you have control over which vertices are used to form the triangles, which can make a big difference in how the object gets rendered.
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