Continuity mistake: As Kono talks to Johnny Kalama in the students' apartment, an orange lava lamp sits on the shelf between them. Each time the camera angle reverses, the wax bubbles in the lamp are very noticeably in different positions and configurations.
Continuity mistake: Danno, posing as a photographer on the beach, snaps the shutter at a bikini-clad girl and quips, "I only wish I had some film." Seconds later, he takes a picture of the suspects that's then used to identify them. The scene is continuous, and at no time did he ever load film into the empty camera, nor did he have another one.
Continuity mistake: Recycled footage is again a bit too obvious here, when McGarrett's 4-door Mercury suddenly becomes the 2-door model he drove in the pilot film. It also causes him to arrive, exit the car and walk into the building wearing a grey suit, but enter the Federal agent's office in the next shot wearing a blue suit.
Continuity mistake: Pool balls redistributed on pool table between the time after the Sargeant breaks and McGarrett casually takes a shot. Especially, noticeable since Tommy, the other player, does not move off the table's edge after the break when two balls comes towards his position and his bottom or pants may interfere with their travel. In the next shot involving the table, those balls are not there and the rest of them seem more evenly distributed across the table.