Continuity mistake: Steve and Danny are searching a suspect's house. Danny picks up a digital camera. He is going through some photos and the LCD display shows 53 photos on the memory card. The counter shows from 53/54 to 50/54. Then he shows Steve other photos and the counter shows only 4 photos. 1/4, 2/4 and 3/4.
Factual error: The aircraft carrier towards the beginning is captioned as being the USS Enterprise (CVN-65), where Lt Rollins is stationed. It is obviously not the 'Big E', but a much smaller escort carrier or amphibious assault vessel. Notable differences are not only the sheer size difference, but also lacks the angled flight deck with the protruding catapult brakes, the second port side aircraft elevator and both the superstructure and bow shape are wrong.
Continuity mistake: When McGarrett is behind the curtain, preparing for the charity fight. McGarrett and the injured fighter, Victor Boriero, share a joke about the dislocated shoulder. Boriero stands behind Lori. McGarrett says "Besides, I'm the one who dislocated your shoulder." Lori giggles, turns to share the joke with Boriero. Boriero says "Yeah, I didn't forget." Lori turns back to face McGarrett (camera shot from behind), and in the next camera shot (camera shot from in front) she turns back to face McGarrett again.
Character mistake: In episode 6-6 Steve explains to Danny that a 'klick' means a kilometre, 0.62 of mile, to which Danny replies: "Oh, thank you, G.I. Jerk, for the pedantic, uh I know what a klick is." In this episode, when Steve again uses the term 'klick', Danny replies: "You know, no-one can understand you when you say stupid things like klicks.", which prompts Kono and Chin to give the exact same explanation as Steve did in season 6.
Factual error: Five-0 brings up a map of all nuclear power plants in Western Europe that is completely inaccurate - most of the trefoil markers in Great Britain are placed nowhere near nuclear installations, and has 3 in Ireland (which doesn't have any nuclear reactors).
Factual error: In episode 17, Danny's Camaro is subjected to a number of bursts from a mini-gun, riddling it from stem to stern. In episode 18, Danny's daughter mentions that he had just had it repaired. There is no way an insurance company would not total that vehicle, since it would require replacing or using "Bondo" on virtually every body panel, not to mention mechanical repairs.
Continuity mistake: When Steve and Danny go to Dr. Yang's office and find evidence of a struggle, they follow a blood trail out the back door. Danny starts to put gloves on as he stoops down to pick up a wallet on the ground. He only has one glove on before the camera angle switches to the view from behind him, then suddenly he's wearing gloves on both hands as he reaches for the wallet.
Continuity mistake: A Texas Ranger spreads peanut butter on a suspect in a sugar cane field. The suspect is tied up on the ground and mostly on lying his back and right side. He spreads the peanut butter on his left arm, head and chest. In a later scene, the suspect is taking a shower and you see lots of peanut butter on his back, both his arms and the back of his head.