When Chin is punching the suspect in custody, between shots, the blood stain on the suspects vest changes between shots with Chin and Lou.
While investigating the inside of an abandoned Challenger 604 aircraft that Steve and his girlfriend Lynn find in the jungle, Steve mentions that the aircraft's transponder has been turned off. With the aircraft shut down, it would be impossible to know if its transponder is turned on or not. Also, while explaining the situation to Lynn, Steve points to an emergency air driven generator (ADG) test switch rather than the radio unit that actually houses the transponder.
The shooter is using an American WW2 era M3 "grease gun" submachine gun with standard magazine, which has a capacity of 30 rounds. The shooter expended far more than 30 rounds in the initial series of shots after the plane was discovered and never reloaded.
In the football game scene immediately after McGarrett and his new girlfriend put the bad guys on the boat, all the numbers on the back of the blue team are backwards.
Much was made about Chin and Grover being over 30 miles away from the home with the kidnapped person and having limited time to save him, yet they drove in Chin's vintage Mustang instead of using a helicopter.