The theme park in the movie is Paramount's Great America in Santa Clara, CA. Paramount is the production company and distributor.
The Annihilator 2000 shown off by Serge at the security convention is actually a dressed up 5.56mm Colt M16, with extras.
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 similar to the Cylons from "Battlestar Galactica" (1978).
While Harold Faltermeyer did not return to scoring duties on Beverly Hills Cop 3, 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 was suppose to be in the vein of previous Faltermeyer/Forsey Beverly Hills Cop techno-pop stadium anthems such as "The Heat Is On" and "Shakedown".
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.