In an interview for Red Bull Music Academy, held in Tokyo October 22, 2014, Composer Harold Faltermeyer stated the anthem from Top Gun (1986) was something he originally composed for a dream sequence in the movie, but friend Billy Idol, who was recording close by, stopped in and told him it would be great as the theme for Top Gun (1986), so Harold dropped it from this film.
The award banquet Fletch interrupts is in honor of Fred Dorfman. Fred Dorfman the name of Kent "Flounder" Dorfman's brother in National Lampoon's Animal House (1978), which was originally going to feature Chevy Chase as Eric "Otter" Stratton. Otter was eventually played by Tim Matheson, who also appears in this movie as Alan Stanwyk.
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 The Godfather (1972) when movie director Jack Woltz (John Marley) finds the horse head in his bed.
Irwin Fletcher's daydream of playing in the NBA, was based partly on another "Earvin"; former Los Angeles Laker Magic Johnson. In the movie's promotional poster, Fletch's team ID card bears the name "Magic Christian" (a reference to The Magic Christian (1969), a Peter Sellers movie based on a Terry Southern novel).
When Fletch (Chevy Chase) and Gail Stanwyk (Dana Wheeler-Nicholson) confront Alan Stanwyk (Tim Matheson), and he says he's going to kill them both, Fletch says, "Oops". To which Gail says, "'Oops'? What do you mean 'oops'? What are you saying 'oops' for?" This line is from an old Bill Cosby routine about a doctor operating on a patient and then saying "Oops" during the operation.
When Fletch tells Frank that he is quitting, he says that he's going to try out for the Lakers, because, according to Fletch, "they need a good power forward". In 1985, the Lakers' Power Forward was Mitch Kupchak, who would go on to become the General Manager of the Lakers.
The trivia item below may give away important plot points.
Continuity issues. When first going to the racket club, his racket has no cover. Later while trying to teach her how to hit the ball, it has a cover. When returning to change clothes after meeting with the President of the airline, he has a straight tie, while during the meeting he had a bow tie. This, however, is a goof, and not a point of trivia.