(at 33 mins) After Jason pours fuel over his hostage's head, close shots of her face show it wet, while a larger shot show her face and shirt completely dry.
When checking the laptop in Jason Duclair's hotel room, McGarrett says he's staying in room 2104. In the next sequence, we see Duclair getting off the elevator on floor *18* and enter a room.
Agent Millford recovers a camera from the wreckage of the fire, stating the camera was used for a "live feed". The camera is a GoPro HD HERO2, which is not capable of wireless live feed to an external source without a Wi-Fi BacPac, an extra accessory that was clearly not in use. And the footage the unsub was shown watching moments later was clearly not High Definition footage, which the camera in use is capable of.
In the opening scene, the couple trapped in a room on fire is trying to exit an external door. They continually push on the door that should open inwards. At no time do the couple step back and tug on the door. The plank nailed across the outside would have no effect on an inward opening door. The hinges for the door also cannot be seen on the inside (likely shot in a fireproof studio set) or the outside (probably a real house).
When playing golf, Steve swings the club back, but the ball flies off the tee without him hitting the ball.