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)
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.
Continuity mistake: Watching the old football game, when number 5-O gets tackled, Kono takes a handful of popcorn that she already took in the previous shoot (a close-up on Scott Caan). (00:39:15)
Continuity mistake: Kono and Danny do a bit of theatrics distracting Frank Salvo and his men that are about to waste cousin Sid. The henchman behind the Samoan gang member is not touching him in the wide shot, but has both hands on his shoulders in the closer cut. (00:34:15)
Continuity mistake: Kono just entered the casino posing as waitress-entertainer. She is snooping around and a guy promptly shoos her back with the others. She does a sassy lil' move with her right hand...but it's the left hand at the cut. (00:28:25)
Continuity mistake: When Danny and Steve leave Joey in the shark cage, he looks at them panicked grabbing the side with the ladder, but when they take off, he's clinging to the opposite side of the cage. (00:22:35)
Continuity mistake: At the pizza place, there's a remote in front of the owner when the two detectives arrive. Nobody touches it, but when Scott Caan grabs it, it is in a different spot of the table. (00:20:10)
Continuity mistake: After the opening, Kono check out of the unidentified victim. In close-up his torso is fuly covered, in the wider shot his jacket is open showing bare skin between jacket and wifebeater. (00:04:55)
Continuity mistake: When Danno talks about tennis and is interrupted by his daughter he tells her "You're supposed to be paying attention" with the foam hand at the side of her head, which disappears at the cut. (00:01:40)
Continuity mistake: When "Uncle Chin" introduces himself to Grace, the kid's pigtails move from the front to the back of her shoulder, back and forth between shots. (00:01:05)
Continuity mistake: Danny and Steve are driving from the hotel to the contractor's house. Every time the camera cuts to Scott Caan, Alex O'Loughlin's hand is in the foreground on the same spot at about 1 o' clock of the steering wheel, regardless of what his character is doing. In the second part of the conversation (after the 'fear of death' mention) he even blatantly drives with his left arm, but still we see just a right hand during Caan's close-ups. (00:17:10)
Chosen answer: They are Junior's SEAL buddies.