There is some mystery in this film, which keeps one somewhat interested. I think the comedy is supposed to be in the brash comments by Ned Sparks as Inspector Riordan. That type of humor may have had a slight following in its day, but clearly not much or there surely would have been many more films made with it. But, just as much in holding one's interest as the mystery, is the absolute dumbness of the cast overall. That is, in the roles being played. I can't think of any crime or mystery story I've ever read or seen in a movie, in which so many people lied outright, with little thought, to the police investigator. And, for no apparent reason. It almost seemed toward the end as though the film was intended as a mockery of the law and crime stories. But it wasn't quite clever enough to be satire.
Well, "Private Scandal" is a murder mystery that gets solved in the end. But, after a few minutes of the opening scenes to set the stage, the film soon became little more than a series of short encounters of Riordan with the various other members of the cast. There seemed no end to little discoveries so that it gradually becomes clear that Cliff Barry wasn't the only person who knew anything abut B. J. Somers' demise. And, Barry was also the biggest and multiple liar of the bunch. Sure, Phillips Holmes played the character as jittery, nervous and discombobulated. But his decisions and actions from the start showed a person who was more stupid than reasonable. Imagine anyone not knowing that the police would be able to determine that Somers had died the night before, not that morning.
There was too much of this type of kindergarten thinking and behavior in this script. Imagine that so many employees would say they thought they had seen a mysterious man who was with Somers that morning. Remember that Inspector Riordan questioned them individually. Yet they all fabricated such a lie. And what about the disconnect from the night before when Simons and his love are surprised and the screen goes blank? Strictly kindergarten story-telling.
Judging from the plot, screenplay and various cast members, I would guess this was a movie done by the B unit at Paramount. Zasu Pitts would have a very long career in films with many, many to her credit, bukt no memorable roles. Most of the rest of the cast, except for Sparks, were hardly known much beyond the time of this film.