Starring: Raymond Burr, Barbara Hale, Ray Collins, William Hopper
The Case of the Hesitant Hostess - S1-E29
Factual error: Supposedly, heroin is being smuggled into the country in secret compartments in women's purses, but the quantity of heroin that could be concealed in such a way would be so small as to be very unprofitable for the smugglers.
The Case of the Wayward Wife - S3-E13
Revealing mistake: Perry and Della step into an elevator but there is no line in the floor between the floor they are on and the elevator floor. It's continuous.
Hamilton Burger: Incompetent, irrelevant, and immaterial.