Mathnet extensively spoofs the long running radio and TV franchise "Dragnet," which provided its iconic theme music for use in this show. Some examples of parody are: the character Joe Friday is spoofed in Kate Monday and Pat Tuesday, and Chief Thad Brown is spoofed in Chief Thad Green.
In addition to his unseen wife Martha, George had a neighbor in Los Angeles named Mr. Beasley, who is never seen in Mathnet shows. However, Mr. Beasley appears in cartoon form in the Square One Television (1987) segments with Dirk Niblick, another mathematical detective. The animated Beasley often talks about his unseen neighbor George Frankly, and is voiced by Bob Arbogast, who makes a guest role in Mathnet: The Case of the Missing Air (1988) as radio host Byle Dupe, of whom Mr. Beasley is said to be a fan.