In the final scene, Steve McGarrett and Joe White are standing outside, in uniform, saluting and "uncovered" - meaning they weren't wearing their uniform hats. This is strictly against regulations in every military service.
After finding a severed hand in the ocean, the medical examiner states that he found elevated levels of lead in the residual blood. He states that this means that the victim was shot before he lost his hand. Five-O later finds the bullet on the boat, which indicates that bullet passed completely through the victim. The only way you could get high levels of lead in your system from a bullet is if you were shot, the bullet was never removed and the lead would leach into your bloodstream over months or years. Since the bullet had passed through him, the victim would have had very little to almost no lead in his system.
While rendering honors to the recovered Navy Captain, McGarrett and and White are not wearing covers (hats) outdoors. This is a violation of military uniform protocol. Their covers are hanging on their belts. Additionally, they salute the casket while not wearing their covers. A salute is not rendered outdoors while not wearing a cover.
When Joe White and Steve are about to go deep diving, Joe tells Steve about the danger of suffering form narcosis while having those thoughts. When you practice "deep water diving" you replace the nitrogen in the air with helium, so there is no chance that anyone can suffer from "Nitrogen Narcosis".
When the WW2 Ambulance is recovered from under the ocean, where it had been since 1942, and placed on the dock, the tires were still intact and inflated. They would not have remained inflated and airtight after 69 years.
The 1939 Packard ambulance retrieved form the ocean was actually a 1946 or 1947 Ford panel truck.