When Catlin opens the safe in his private suite, all the bags of diamonds are lined up in a single row. When MacGyver opens the safe a little while later, one of the bags is on top of the others.
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.
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 Catlin places a bet for Chris on the roulette table, the ball lands on 25, but the croupier says, "10 black. The lady wins."
One can't pick a door lock one handed; two prongs (one in each hand) are needed to manipulate the lock's tumbler to get it to open.
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.
When MacGyver enters the vault in Catlin's suite the wire that opens the wall safe door is visible.
MacGyver could not have known how to shape the coat hanger holding the mirror to perfectly fit over the security camera he had never seen before.
When Catlin opens the vault and it shows all of the doors opening you can see a string pulling open the left facing cabinet.
When MacGyver pushes a car with parachutes out the airplane one can see the cameraman jump out after the car.
When MacGyver drives the car out from the airplane a camera is visible in the passenger seat.
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.