Della notices that the terrified typist has disappeared at 7 o'clock, which is the same time that Patricia Taylor later testifies that she was at the restaurant to meet with Duane Jefferson. In the picture taken at the restaurant, Mrs. Taylor is in an evening dress, an outfit different from what she was wearing at Mason's office.
The body rolled off the pier is obviously a stunt double wearing a skinhead wig and lacking the victim's mustache.
When Perry, Della and Paul are examining the two photographs in Perry's office, it is obvious that everyone in the background of the pictures are exactly the same, and in exactly the same positions. This would be impossible unless the photographs were staged or rigged somehow.
Perry's client's alibi is that he was at a restaurant and spent the evening with a woman he refuses to name. Paul finds photos taken at the restaurant of Perry's client and two different women. And yet they don't investigate and try to confirm the alibi by following up with the restaurant staff and photographer.
The murderer is involved in a scheme to steal half a million in diamonds and yet gets involved in a blackmail scheme with the senator's wife for a comparative small sum that creates a lot of extraneous attention.