This is one of several episodes where Jessica Fletcher only appears briefly as the narrator of a frame story. In this case, the episode centers on the investigation by one of her many friends and acquaintances, Lt. Jake Ballinger. These episodes that featured Fletcher only as a narrator were primarily used as a device to give an overworked Angela Lansbury a bit of a break.
Freemont University would be seen again in the 1990 movie Columbo Goes to College.
This episode served as a pilot for a potential spin-off series. It was, predictably, not picked up.
In a ridiculous scene early in the episode, Lt. Ballinger discharges a firearm in a crowded lecture hall just to get the attention of talkative students. Even assuming that the gun was loaded with blanks (that is not clear from the scene), such an action would have been unthinkable in a 1980s university. If an instructor fired a gun in a classroom, again even loaded with blanks, they would have been summarily fired and would likely have faced serious criminal charges. It seems likely that an experienced police lieutenant would know of the potential repercussions of discharging a firearm in a classroom and would have avoided doing so for such a frivolous reason.