In a previous, excellent answer it was proposed that it might be helpful to subdivide some triangles in my mesh at certain times during the animation to prevent them from overlapping adjacent faces when the mesh is very highly distorted. It's best to look at the question and answer there now.
OK you're back. The trajectory of the ~10,000 vertices of the original icosphere mesh are pre-calculated and stored in a NumPy array. A "badness" detector could search for highly stretched edges, but then what? If it inserted real vertices, I think it might be tricky to try to remove them later, and keep the rest lined up with NumPy. I could try to figure out a way to script that, but I wonder if there might be other ways, or possibly something existing in Blender already?
I am re-linking @TLousky 's image here: