Production was temporarily shut down to allow the Paramount top brass the chance to get to grips with the film's spiraling budget. Originally estimated at $55 million, it was soon in excess of $70 million. Of that budget, $15 million was Eddie Murphy's paycheck.
The Alien Attack ride that Janice (Theresa Randle) demonstrates to Axel when he first comes to Wonderworld is actually the Earthquake section of the Studio Tour at Universal Studios in Hollywood. The alien robots are the Cylons (from TV's Battlestar Galactica (1978)) from a section of the old Universal Tour "Battle Of Galactica."
Initially, the plot for this film would've concerned Foley, Rosewood, and Taggart (John Ashton) going to London to rescue Capt. Bogomil (Ronny Cox) who was being held hostage by terrorists during a International Police Convention. However, numerous problems such as scripting issues and the budget, caused pre-production to drag out the point that both John Aston and Ronny Cox had to drop out due to obligations to other pending film projects.
Alan Young, who plays the Walt Disney-like "Uncle" Dave Thornton, owner of the Wonderworld theme park in the film, has been the voice of Scrooge McDuck since 1983 and is more commonly addressed as Uncle Scrooge by his great-nephews Huey, Dewey, and Louie.
Disney composers Richard M. Sherman and Robert B. Sherman, who wrote the Wonderworld song for the movie, both filmed cameos. Robert was among the old men discussing the murder at the bar, but Richard's cameo as the grand marshal of the Wonderworld parade was cut out.
Among the rejected ideas for "Beverly Hills Cop III" included a Robert Towne screenplay idea (one in which Axel Foley has to deal with his celebrity cop status), a scenario teaming Eddie Murphy with Sean Connery as a Scotland Yard detective, and another Axel Foley-in-London idea where his Scotland Yard counterpart would have been played by John Cleese. The last story would have involved a British gangster loosely based on the real-life Kray brothers, who was captured in Detroit and transported to London by Paul Reiser's Jeffrey, and Axel would have gone overseas after the gangster's henchmen broke him out of custody and murdered Jeffrey. This concept was scrapped because producers Don Simpson and Jerry Bruckheimer decided it was too close to the storyline of the Michael Douglas' film Black Rain (1989).
When John Ashton was unable to reprise his role of Taggart, his part was re-written as John Flint (Hector Elizondo) and dialog was inserted to explain that Taggart had retired and moved to Phoenix. Ronny Cox was also unable to reprise his role of Bogomil due to commitments to other projects, however his absence is never addressed in this movie, nor is he mentioned at any point. Both Ashton and Cox due have subtle cameos in this movie, in the form of a picture on Rosewood's desk of Foley, Taggart, Rosewood, and Bogomil on a fishing trip. This is the very same picture which also appeared in Beverly Hills Cop II (1987) on Bogomil's and Foley's desks.
In an interview in 1994, Eddie Murphy said that the film is "different from the trilogy's first installment because Axel is more mature and no longer the wisecracking rookie cop." He wanted to be taken seriously as an straight action star like Wesley Snipes and Denzel Washington.
In an interview with The A.V. Club in 2009, Bronson Pinchot claimed that Eddie Murphy "was really depressed" at the time the movie was being filmed, claiming that Murphy was low-spirited and had a low energy level. He was depressed that most of his most recent star vehicles had either underperformed or bombed.
While Harold Faltermeyer did not return to score this film, his song co-producer from the previous franchise entries, Keith Forsey, did produce and co-write a new song. "Keep The Peace", performed by INXS and in the vein of previous Faltermeyer/Forsey "Beverly Hills Cop" songs such as "The Heat Is On" and "Shakedown."
Eddie Murphy said he thought "Beverly Hills Cop III was infinitely better than Beverly Hills Cop II (1987)." He then later claimed during an interview in 2006 on Inside the Actors Studio (1994) that he felt the third film was "atrocious" and such a disgrace that "the character was kind of banished for a while [from Hollywood]." He said he felt the third film did not reveal enough of the "edginess" of Axel that was present in the first two films. He also said he hopes to return the edgy qualities to the character when he reprises the role next time, and is going to pay more attention to the development of the project and its quality.