As Steve clears the top floor he opens the bathroom door. From outside the toilet seat is up but when they zoom in for a closeup the seat is down.
McGarrett is eating pancakes with Grover in the first scene. When he gets the check from the server (2:06), he has part of a pancake left on his plate. Seconds later (2:12), his plate is empty. A couple seconds later, (2:14), the pancake is back on his plate.
The driver's side mirror on Zagar's vehicle gets folded in during the first collision. It changes from folded in to extended throughout the chase.
The US Marshal's Service, not the FBI, handle protected federal witnesses.
The shootout exceeded the magazine capacity of the weapons used, and no one reloaded.
An FBI agent failing to identify himself and pulling a gun on an HPD officer under the circumstances shown would at a minimum be censured by the FBI and likely be criminally charged by state authorities.
The NCIC has information about criminals and crimes, not FBI agents.
Set construction: the hook and loop on the bathroom door are installed on the outside, not the inside.
When hanging up the call from the FBI, the screen disappears before Steve hangs up.
When the federal government relocates a witness they do not resume their life doing the same line of work. They would not place a protected witness that had been a law enforcement officer in a law enforcement position. They certainly would not allow a witness to remain in the program if the witness joined a high-profile unit such as 5-0.
After Grover's son gives him a folding pocket knife, Grover makes a comment about how everything will be all right because he now has a corkscrew, a toothpick, etc. That would be true if it was a Swiss Army style knife, but it was a simple Buck style folding pocket knife.