Other mistake: Nuzo saved Magnum's life in Afghanistan, cauterizing with gunpowder a big deep wound that hit a blood vessel in his chest. Throughout the whole series, Magnum flaunts all the time his flawless torso, with no scars whatsoever. (00:20:40)
Other mistake: When Magnum asks Higgins a favour, she tells him that he already asked for one 'last week'. She repeats that later in the terrorist's car. With that being a reference to the previous episode, it means that her arm, literally pierced by a bullet and that she had in a sling, healed completely without as little as a bandage (she is even wearing a sleeveless dress!) in 7 days or so. (00:25:40)
Six Paintings, One Frame - S1-E4
Other mistake: Speaking with Chen, Higgins tells him that she had Robin Master's IT experts "scrub every byte" of the computer Magnum used to upload the report, and there was no security breach on their end. Considering that she is with Magnum when they visit the crime scene that the police is still processing, it'd mean that the experts 'scrubbed' the computer doing a complete forensics analysis in an hour or so - assuming they did it on remote too, since obviously Robin Masters' team is not in Hawaii. (00:13:00)
Sudden Death - S1-E5
Other mistake: During the game at the beginning of the episode, the opposing team (the Pearl City Chargers, white and purple) fields at least two players with the same jersey number 12. The kid protagonist runs past a guy with number 12 at he starts his run, and then dodges another two in front of him, who are present in the same shot - it's not a matter of editing/continuity, at least in that second shot. (00:50:00)
Other mistake: A mayday call is received. It is shown on the moving map display as originating to starboard of the boat Magnum and Higgins are on. They promise to go help but turn to port. (00:01:50)