No Way Out - S3-E3
Other mistake: Higgins is asked if she can hack a security feed from an office. She replies that she can do it, but it will only be audio, no video. When she hacks it, is only video, no audio. (00:14:10 - 00:15:35)
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)
Other mistake: A man kidnaps an IT tech and steals his uniform. The IT guy is quite large - at least a XXXL if not more. When the impostor IT guy walks into HPD Headquarters, he has a very well fitting IT uniform shirt. And he is of average build -maybe a medium size. There is no way he could be wearing the real IT guy's shirt without it looking like a tent.
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)
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)
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: 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)
The Day Danger Walked In - S3-E5
Other mistake: In the middle of the storm, telephone service goes out. Yet later, one of the robbers sees an emergency alert on his phone and says it is getting worse. If cell service is out, there is no way he could have received that.
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)