Factual error: While Fletch is riding with the bikers, they stop at a stop sign where a family in a station wagon roll up their windows in fear. A sign at a service center in the background is the Castaic Junction, which is in the greater Los Angeles area. The movie is supposed to be taking place in Louisiana. (01:12:35)
Continuity mistake: When Fletch goes to visit Calculus in his shack, he knocks on the window and sees Calculus sitting in a chair, wearing boots. The next shot, as Fletch is walking inside, Calculus is now wearing socks and no boots, despite never having left the seated position, nor having had any time to slide his feet out of the boots. (00:35:55)
Continuity mistake: When Fletch goes into the Biker Bar it's pouring rain, but when he comes out minutes later and goes riding on a cycle, it's not raining and the ground is completely dry. (01:09:05)
Other mistake: Fletch complains to Frank that he needs a vacation. Frank replies that he gets one in July, which is 2 months away, making the present day somewhere in May. He later gets a call stating he inherited an estate. Amanda meets with him and is later murdered. The documentation shows she was cremated on March 5, 1989. The cremation should be in May.
Continuity mistake: When Selma comes out of the kitchen with 2 plates in her hands, there's no towel on her arm. In the next shot it's there. When she puts Calculus's plate down it's gone again and in the next shot she's wiping her hands with the towel.