Continuity mistake: Magnum drives the Ferrari to the National Memorial Cemetery of the Pacific with the sky being overcast. That's just the establishing shot though, because the sky is blue and the sun brightly shines in the rest of the scene. (00:07:45)
Continuity mistake: Magnum meets his new client. He asks "Have we met somewhere?", with his fingertips touching. "We were briefed together once, at Da Nang" the client replies, while Magnum lowers his hands and puts them on his hips. New shot, and he is again in the previous position, with the fingers touching. Similarly, the client mistakenly has his arms crossed a couple Transitions later when he says the two teams never hooked up. (00:08:30)
Visible crew/equipment: After Taylor gives Magnum the bottle of champagne Magnum heads to the couch, and when he sits down the white T-mark is visible on the floor, in front of Taylor. (00:15:10)
Continuity mistake: Taylor asks Magnum if anything happened to Linda. Magnum says "No!" twice; in the first shot his left arm is on top of the back of the couch, in the next one it's slumped into one of the pillows. (00:15:20)
Continuity mistake: Tailing Cam Chung with his Ferrari, Magnum does not have to go too far, seemingly, since he keeps meeting the same people over and over. A guy with a red T-shirt under a plaid shirt, a woman with a purple dress, one man with a blue tee and a single horizontal stripe, a man sporting a 'stache and wearing jeans and a pale blue Hawaiian shirt, etc. (00:21:00)
Continuity mistake: When Ed Kanfer's widow tells Taylor "But he's gone", her hands are not on his shoulders, where they appear in the next shot. (00:32:10)
Continuity mistake: There's obvious recycled footage to pad the episode during the approach of the chopper to the "fishing spot"; they take off with a chopper with normal skids and no doors, but the one flying over the ocean has flotation pads and its doors in place. The pilot is also wearing beige flare pants and not TC's jeans. The same mistake happens when he flies Magnum over, same recycled footage. (00:35:45)
Audio problem: The chopper is so noisy that people in it can barely talk to each other over the noise (as made clear abundant times in the series, including the previous episode when they "muted" Higgins switching off his intercom), but Thomas and TC are having a conversation while the helicopter is hovering meters above and Magnum is still with his feet in the parking lot. TC's lines are also neatly dubbed in. (00:39:00)
Other mistake: In less than 30 seconds of uninterrupted dialogue, the bomb advances from 1:05 to 11 seconds to go. (00:45:50 - 00:46:15)
Factual error: At the end of the episode, they bring flowers on the tomb at the Memorial cemetery, but given the crime committed, the vet would have been denied to be buried with those honors.
Plot hole: Taylor has the case scouted in such a way that you'd wonder what did he even need Magnum for in the first place; somehow he knows that the bad guy is in Hawaii (which is where the widow happens to live too), he knows he is seeing some girl and who she is, and got a picture of her too. If Magnum did what he asked, he would have arranged a meeting with her away from the gorillas - he does not insist to accompany him or anything of the sort, and in fact he needed only TC for that. Also, somehow Taylor knows as well where the bad guy's hideout is, but Magnum never returned with that information.
Plot hole: Taylor sets a timer on the claymore mine to make it explode within 10 minutes instead of by passage or by remote control, which is already pretty inefficient considering he went through the trouble of altering the original design, but even with that considered, it's inexplicable how Taylor knew that his target would be at that particular gazebo of the large estate, precisely at that time, within 10 minutes. To even get there he needed to ask TC, surely he's not privy to the victim's every habit nor schedule.