A “fishing expedition” is an investigation that looks into many matters in the hope of finding at least one piece of incriminating evidence. The investigation is “fishing” for whatever evidence it can “hook” on someone.
 
“The Ohio republicans who wanted the United States Senate to go on a fishing expedition in the hope of convicting Senator Payne of bribery” was cited in print in 1886.
 
   
Wiktionary: fishing expedition
Noun
fishing expedition (plural fishing expeditions)
1. (idiomatic, law, US, informal, pejorative) A non-specific search for information, especially incriminating information.
 
Meriam-Webster Dictionary
fishing expedition noun
Definition of FISHING EXPEDITION
1:  a legal interrogation or examination to discover information for a later proceeding
2:  an investigation that does not stick to a stated objective but hopes to uncover incriminating or newsworthy evidence
First Known Use of FISHING EXPEDITION
1874
 
7 May 1886, Springfield (MA) Daily Republican, pg. 4, col. 1:
The Ohio republicans who wanted the United States Senate to go on a fishing expedition in the hope of convicting Senator Payne of bribery will be highly indignant at the decision of the republican caucus that their charges are not explicit enough to warrant investigation.
 
25 November 1890, New York (NY) Times, pg. 5:
... further, that the Grand Jury must have a definite accusation to work on, just as a Coroner must have a body before he can hold an inquest, and that it is not empowered to go on “fishing expeditions,” as it is doing in this case.
 
10 March 1918, New York (NY) Times, pg. 6 headline:
Federal Court of Appeal Intimates Investigator Is on “Fishing Expedition” in Counsel’s Vaults.
 
Google Books
A Dictionary of Modern Legal Usage
By Bryan A. Garner
New York, NY: Oxford University Press
2001
Pg. 361:
fishing expedition is a CLICHE used to describe (contemptuously) an opponent’s attempt, through discovery, to elicit information that might help that opponent. The phrase ought to be given a rest, as the Supreme Court urged long ago: “No longer can the time-honored cry of “fishing expedition” serve to preclude a party from inquiring into the facts underlying his opponent’s case.” Hickman v. Taylor, 329 U.S. 495, 507 (1947).