Norman Briggs, the character played by Michael Tucci, was scheduled to be murdered by a man seeking revenge against Dr. Sloan in the 4th season finale "The Murder of Mark Sloan". Tucci begged producers not to kill him off and they agreed. The following season he was no longer on the show and no explanation was given as to where his character went.
In one episode a stunt with a motorcycle was required. But the production team didn't have the budget to perform this stunt in real life. Dick van Dyke, being a computer animation enthusiast, created the special effects on his home computer using the LightWave 3D animation software and they were used on the show. He was paid $200 for creating the sequence.
Mary Tyler Moore was sent a script once, for her to make a Guest Star appearance in an episode of 'Diagnosis Murder', but she turned down the script, because she felt it didn't suit her. Dick Van Dyke also never appeared in her hit TV series 'The Mary Tyler Moore Show'. Both had previously co-stared in their TV show 'The Dick Van Dyke Show'