The Beechcraft 2000 Starship seen at the beginning is a very rare aircraft. There are only about 5 registered worldwide.
The airplane shown at the beginning of the film is a Beechcraft Starship, a twin turboprop (as Jessica Fletcher calls it, a jet) executive aircraft. (A turboprop is a jet engine.)
Chad Everett plays an abusive husband in this episode and in real-life once referred to his wife as an "animal" that he owned while being interviewed by Dick Cavett, prompting fellow guest Lily Tomlin to walk off the set.