Factual error: A taxi pulls up to a private jet at an airport in Hawaii. A public taxi cannot just pull up to an aircraft at an airport. It needs clearance to access airside areas. (00:21:05)
Other mistake: Magnum is shown in Captain Greene's office in uniform. He is wearing a US Navy Parachuteist Badge, his SEAL trident, and has the rank of Lieutenant. In the show intro section, he is always shown wearing just the trident, and has the rank of Lieutenant Commander. Was he demoted? (00:03:15)