Chevy Chase has mentioned in interviews that this is his favorite of his movies, because it let him be himself.
Gregory McDonald, the author of the Fletch novels, had casting approval over the film. He rejected Sir Mick Jagger and Burt Reynolds before he decided on Chevy Chase for the lead.
At the end of the movie, when Fletch hops over the fence and walks along the pool area to gain access to Alan Stanwyk's house, it is the same house used in Le Parrain (1972) when movie director Jack Woltz (John Marley) finds the horse head in his bed. In another "Godfather" reference, one of the aliases Fletch uses is Don Corleone, the Godfather played by Marlon Brando in that movie.
The award banquet Fletch interrupts is in honor of Fred Dorfman. Fred Dorfman was the name of Kent "Flounder" Dorfman's brother in American College (1978), which was originally going to feature Chevy Chase as Eric "Otter" Stratton. Otter was eventually played by Tim Matheson (as the film's makers didn't want it to appear as a Saturday Night Live (1975) movie), who also appears in this movie as Alan Stanwyk.
While in Chief Karlin's office, Fletch punches a framed photo of the Chief with Los Angeles Dodgers manager Tommy Lasorda, saying "I hate Tommy Lasorda!" In a sequence that was filmed, but cut, Fletch had another fantasy moment akin to the Lakers Dream where he's pitching in the World Series and Lasorda pulls him from the game. While the sequence never made it into the movie, there are existing production stills of Fletch on the pitchers mound and Lasorda coming to take the ball away from him.