This anthology consists of tree novellas:A Window for Death.
A prodigal son
An estranged member of a family comes back after a long time for a reunion.
The said reunion was very short-lived as he dies from pneumonia. The late guy stroke it rich, but now his siblings see possible complications with their inheritance and one of them even suspects foul play in his brother's death. Nero Wolfe is the guy they ended up consulting. Can an obvious case of pneumonia be a murder?
An interesting deduction made by Wolfe from seemingly a trivial matter which nonetheless did not fit with facts solved the mystery. I am not sure if this trick would work in real life. Immune to Murder.
A diplomat from an unnamed country with which US is trying to establish good relationships express his desire to do some fishing and asked for Nero Wolfe to prepare his well-known Trout Montbarry.
The latter thinks his patriotic duty is to oblige the request. A dead body promptly shows up in the isolated fishing location.
Archie Goodwin tries fishing. He is not very successful with fish, but when it comes to finding dead people his luck(?) is still with him. Too Many Detectives.
Believe it or not, there was a time in US when illegal wiretapping was a big deal, regardless of who did it.
So a large group of private detectives involved in one were summoned to testify in from of a special committee. Nero Wolfe - and by extension Archie Goodwin - were unwittingly involved in one such activity. Suddenly the man who tricked them into doing illegal wiretapping shows up - only to be promptly killed. The detectives in the group I mentioned are the only suspects with dynamic duo having a distinction of being the prime ones.
As title suggested there were too many detectives involved for the crime to remain unsolved for long. In fact Archie Goodwin found himself with nothing do to most of the time. Nero Wolfe meets a competent female PI up close and personal. Archie briefly but seriously began entertaining the idea of his boss being enticed by her into marriage.
My usual description of Nero Wolfe novellas applies here as well: fast read and entertaining.