Magnum was tortured during his military days requiring a wound to be cauterized with gun powder, yet there is no scar at all when Magnum is later seen shirtless. He would have had deep scars from such a procedure.
Magnum says that he was a POW, but the picture of him shown at the end of the opening sequence doesn't show him wearing a POW ribbon.
The gold bar that Magnum found is too large to be 1 kilo (2.2 pounds). Gold is extremely heavy for its size, and the bar looks as if it would weigh closer to 12-13 kilos.
In the final chase Magnum swerves the Ferrari much further than the 90 degree angle it ends up in when he shoots at the truck.
When Higgins calls Magnum on her way to the hospital, he doesn't swipe the phone to answer the call.
When Magnum is exploring the wrecked ship, you can see the water's surface in one shot despite him being on the ocean floor.
During the drive to the final chase scene Magnum is talking to Higgins on the phone. The driver's window is partially up, but as you see the view from the inside of the car the window is shown down. This happens back and forth during the phone chat.
While Thomas is driving along the H-3 Highway talking to Rick on the phone, flashing blue lights of police cars behind him can be seen out of the rear window. No police are visible in the overhead shot.
Higgins would be arrested, prosecuted, and convicted for computer crimes regularly quickly.
Magnum breaks a cardinal rule of diving: Never dive alone.
No Navy SEAL would wear dress whites with stubble on his chin. He would shave.