Character mistake: After distracting the guards, Danno tosses a grappling hook onto a ledge and climbs the side of the building. He then goes about his business, carelessly leaving the hook and rope dangling from the ledge for all to see. For a seasoned 5-0 team member, that's pretty sloppy covert operations.
Plot hole: As a security test, McGarrett secretly has several dummy bombs planted in the court building, then later shows the governor where they are. Each time he pulls one of the devices from its hiding place, citizens in the courthouse stroll casually by without so much as glancing at the loudly-ticking "bomb." No one knew about the test, so McGarrett's bombs should be attracting some attention, if not causing outright panic.