I (a nervy newbie) think I may have the answers to the missing exam and the tossed flat. In the episode from season two, "Trove", the one about the politician, the beauty queens, the man who fell on the car roof, the Masons, and incest, it was strongly indicated that Sergeant Strange, (eventually Chief Superintendent Strange), was invited to join the Masons. At the end of that episode, there was a white-gloved hand passing a small notebook to a man's hand with a Masonic pinky ring. The notebook of the man who fell on the car roof went missing when the crime scene was being processed. I think Sergeant Strange delivered it to his brother Masons. And eventually he became Chief Superintendent. (Even before being recruited by the Masons, he would have had good reason to disappear Morse's exam.)