When Catlin checks on his vault after the alarm is set off, he leaves the doors to the diamonds open and leaves and closes the main door. When Mac goes in the vault after that, the doors where the diamonds are is closed instead of open.
The episode supposedly takes place in the U.S. Virgin Islands, but during the end scene when the car is parachuting out of the plane, below we see a flat, almost barren landscape. Nothing at all what a tropical island looks like.
Early in the episode, MacGyver says that Catlin is untouchable and can't be arrested. While this would be true in other parts of the Caribbean, since the episode takes place in the U.S. Virgin Islands, Catlin could easily be arrested by federal law enforcement (FBI or U.S. Marshals), as it the Virgin Islands are still part of the United States.
When MacGyver was trying to defeat the laser barrier in Catlin's room he uses a plastic tube. But
as soon as he put one end of plastic tube into a laser hole it should have broken the electric beam and triggered the alarm. But it didn't.