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.
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: 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.
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: Danny is taking to some Victoria's Secret models on the beach. They ask to see photos of his daughter. He is talking to them and he pulls out his cell phone from his pants pocket. Next shot, you see him reach for his pocket again and once again he pulls out his phone.
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.