It might be a good philosophy and practical for classroom teaching, but he needs to use the advantages electronic media offers and do some editing. At least to remove anything that's really going to throw a student off and possibly even discourage them.
Why not just re-record the video, or design the videos such that they can be stitched together from small manageable sub-videos that can be easily and quickly re-recorded. There are plenty of times when he "clears the screen" and these would be perfect opportunities to edit together "good" sub-videos in the lesson.
I don't see why you would want to leave the mistakes in there. Someone might not grasp the correction!