Continuity mistake: Inside Steve's office, Mary says that she would have taken anything from their dad, even disappointment,"because at least it would have been something." In that close-up, her hair is noticeably different than in the rest of the scene, much thinner over the shoulders. (00:19:45)
Continuity mistake: Steve and Danny sit at the diner's where they need to meet with the fugitive's girlfriend. As Danny gives Steve the speech about the "mammal to mammal" interactions he puts his toothpick in his mouth, but it vanishes in the front view, only to be plucked back at the beginning of the next shot. (00:22:35)
Continuity mistake: In the long bickering with Steve while they kinda talk with Sofia, Danny picks up the badge the Steve put on the table, put it down before the cut talking about bad relationship decisions, but in the next shot he's gesturing again with the badge. (00:23:10)
Other mistake: The episode makes sure to mention the real places where the action happens. The fugitive escapes from Halawa Correctional Facility, and dumps the car at Kakaʻako Beach Park, which is about 25 minutes away. Danny and the others arrive at the location way before Steve, who was at the airport, which is roughly 15 mins away from the penitentiary (kinda odd that they'd happen to be even closer than him, but fine). They have then the footage to investigate, the guard to talk to, the game of hoops with the prisoners, go back to their precinct, but despite the huge headstart Ellers had, they catch the car that was abandoned "15 minutes earlier." Moreover, Chin calls Danny to tell him about the car only after he already investigated the location and interrogated the witness. It can't even be 15 minutes, because 15 minutes is when the fugitive bought the products from the market, and he still needed to dye his hair.
Ko'olauloa - S1-E6
Continuity mistake: At the end of the episode, the surfers are in the bay to spread Ian's ashes. Ben lets go of Kono's hand and is handed the urn with the ashes by the man to his right. He removes the lid of the urn and hands only the lid back. Yet in the overhead shot immediately following, the urn is back on the board of the man to Ben's right, and there is nothing on Ben's board. He's holding Kono's hand again. In the next shot, he is tipping the ashes from the urn.
Ko'olauloa - S1-E6
Continuity mistake: When McGarrett chases the bad guys' Jeep, his Camaro skids through several huge dust clouds. Immediately after each cloud, however, the car is perfectly clean again. This is visible in several of the very rapid shots throughout the chase. After the chase ends, a coating of dirt and mud (which, incidentally, differs from the earlier shots) appears on the Camaro.
Continuity mistake: When Steve and Danny enter Bar 35 it's daylight, and when they leave after no more than a few minutes it's completely dark.
Other mistake: An important key to the first season's plot is the "dancing men" code on the postcard. We see the postcard several times leading up to Ep 1:13. It shows 3 lines of code containing 4, 4, then 3 characters. In this episode, however, Steve brings out his workings on a yellow legal pad to show the others. There are more characters on his pad than are on the postcard, and some of the characters (for example those with both arms on one side of their bodies) do not even appear in his workings. He claims to have used frequency analysis to work out the code. If one uses frequency analysis on the actual code we see on the postcard, the result can never be Hiro Noshimuri. (00:23:35)
Factual error: Contrary to what Steve says, the U.S. do have an extradition treaty with France, which has been in effect since 2002.
Continuity mistake: During the police chase there are flashing blue lights visible on Chin and Kono's faces during the interior shots, but from the outside of the car only the flashers in the grille are working.
Factual error: Kono is driving a 4-cylinder Chevy Cruze in pursuit of a V-8 Mustang, and manages to stay right behind it.
Visible crew/equipment: When showcasing the empty road as well as Danny's Camaro taking a sharp left for an action scene, there is a camera dead center in the road, and they drive right behind it. (00:28:59)
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 Danny goes to the police station and Grace runs to hug him, her left arm switches from being around his neck to under his arm.
Character mistake: Kono and a lab tech are stopping at several stations to sample their 87 Octane gas, yet at the third gas station he uses the middle pump that reads "Plus" which would be 89 octane - the wrong gas. (00:19:10)
Chosen answer: They are Junior's SEAL buddies.