During the race between Terry Brogan (Jeff Bridges) and Jake Wise (James Woods), whenever both drivers are shown, both of their hands are always on the steering wheel, yet the sound of constant manual shifting can be heard.
In "The Palace" scene where "Kid Creole & the Coconuts" are performing, Terry leaves the main floor and goes into Jake's office. The song playing in the background "Curiosity" skips a beat when heard muffled in Jake's office.
During the race scene between Terry Brogan and Jake Wise, Jake's dog, who is riding in the front seat with him, disappears during the high speed scenes and then reappears at the very end of the race scene. Also, as Jake prepares to pass a motor home, a rear hatch is open on the motor home and then suddenly it is closed.
In the scene where Terry and Jess are arguing on the "ball field" in Chichen Itza, as the camera switches back and forth between the two, in the background behind Jess a group of kids playing ball can be seen at the other end of the arena; when the camera cuts back to her, they're gone, and the next time the camera returns to her, they are visible again, albeit in the very edge of the frame.
When Terry jumps off the boat onto the island where Jessie is, his pants legs are seen to be wet about half way up to his knees from wading in the surf. When next he is seen, just before he gets to where Jessie is standing, his pants are wet all the way up to his knees.
At the start of the movie Terry is wearing dark deck shoes when he speaks to the taxi driver about the photograph. When he speaks to the third person about the photograph he's wearing white Nike trainers.
A dog could never ride untethered in any seat, especially a front bucket seat, of a car racing through traffic and steering and accelerating and braking as violently as happened in Jake Wise's (James Woods') car in the racing scene, without being violently thrown around inside the car, hurt, and/or thrown from the car..
When Brogan finds Kirsch lying dead in the shower the camera zooms in on a close-up of Kirsch's face. You can see that Kirsch's pupils are constricted by the bright light. A real corpse's eyes would be fully dilated.