Continuity mistake: When Steve McGarrett takes the picture of the footprint, what is photographing is different from what was shown earlier; the print and the objects to the left shifted - easy to tell using the tiles as reference, since in the picture the heel of the foot stops right at the line between two tiles, while it went well across it in the original shot. (00:10:50)
Continuity mistake: Danny and Grace get up to go buy some nachos; at the cut, both Chin and Steve's hands have changed position. (00:01:55)
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.
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.
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.
Continuity mistake: In scene where Kono makes origami crane, she sets it down on top of Evan's Ipod. Next shot the crane is sitting next to the Ipod. (00:26:30)
Continuity mistake: In scene where Chin starts reviewing footage of white van attacking, in first shot a wheel from the NSA guy's van has rolled off and comes to rest immediately in front of attacking van's driver side front wheel. In next shot as driver exits, loose wheel is missing. (00:11:20)
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)
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)
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 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.
