Other plot holes
Aside from the one mentioned already (Peter's secretary is supposedly poisoned to keep her from revealing that Peter is the Tarot Card Killer. The plot continues, and we discover that Peter is actually a "copy cat killer", and only killed the last victim (long after his secretary was killed). The man actually arrested as the Tarot Card Killer even reveals details only the real killer could have known. If this is true, and Peter is not the Tarot Card Killer, why was his secretary ever poisoned?), here is another:
When Woody finds the envelope with "Betty G" written on it, it eventually leads to them realizing that Lyman killed Betty G. But why on earth would Lyman write her name on a piece of paper and then keep it in his bag for anyone to find, either before or after he killed her? He had been seeing her for years and wanted to keep it a complete secret. Even if the envelope had held money for her, why would he write her name on it? It seems like a plot point added for convenience rather than reality.
I liked this movie although it isn't one of Woody's tightest scrips for the above reasons. I also thing Scarlett is wonderful as the rather naive young reported; she even snorted when she laughed once!
One more thing: this theme, a wealthy man being blackmailed by a lower class woman that he ends up murdering, has been done in Matchpoint and Crimes and Misdemeanors, and now Scoop. Do you think Woody is obsessed with this idea?