The plot continuity problem mentioned below cannot be accounted for by syndication cuts. In the DVD version, there is also no mention of either Eleanora's job at a night club nor the fact that she had a husband.
There is a second continuity problem, as well. Juliet bursts in on the napping Burke and announces that she has information on "The Davis Case"--the dead girl's current address. When Burke left her early that morning, he was leaving to investigate a "dead brunette". They had only just gotten the girl identified when Burke slipped back home to grab a quick nap, having been out all night. The whole case was wrapped up in one day; it's not likely the news of the girl's identity would have gotten out, let alone the fact that they were trying to find her current address.