Points of light
This happens quite frequently, I am not sure if there is one answer to this. light spots: possibly a star; possibly a pixle of light from the camera; possibly something else; will appear in one frame disappear in another. Should I be marking these as artifacts?
Yes, mark them as artifacts. Those are hot pixels caused (most often) by cosmic rays.
To be honest, I'd imaging marking the hot pixels as artifacts is far more valuable than those obvious erratically moving ones because the software can easily recognize the later (as they don't move linearly) but may have trouble with the former especially if 3 happen to align just right.