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.
Other mistake: When Steve picks up the call from the Governor, his wristwatch points at about half past 10. The kidnapping, he then says getting to the location, happened one hour before, but during the opening his kid Evan whined that it was 6 am. Also to be noted, Steve in typical movie fashion is expositing the mission during the drive in the outskirts of town, as if he'd just have dragged his partner for miles without saying the first thing about the reason. (00:05:40)
Other mistake: The human trafficker Sang Min covers his retreat from the warehouse firing wildly with a Micro Galil. In the time it takes for Steve to shout to the others if anybody is hurt, he somehow already ran all the way to his Mercedes deep up the alley and start it up so it can make a nice screeching noise and ram McGarrett. (00:34:50)
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)