When McGarrett arrives at Burke's hotel, it's a stock shot, as the hotel is incongruent with the view at the very beginning of the show.
After Che Fong uses the metal detector to identify the grave where Peking Man's fossils might be located as that of "F.H. Heller," the first closeup of Heller's headstone is "flopped", i.e. all of the writing is reversed because the film was accidentally printed backwards.
Danno is dispatched by McGarrett all the way to South Carolina just to pose a few questions to one of the still-living Marines of the squad that transported the remains. This is ridiculously odd, as he could have easily garnered the information by telephone contact.
It seems implausible that Parmel, having escaped from San Quentin so recently, somehow had the funds and means to travel to Hawaii.
After the grave marker switch, and the coffin is opened, the mystery Marine's body is noted as wearing Korean War decorations. Yet later, when the gave that the marker was switched FROM is seen, it is for a man who died in 1945, or five years before the action in Korea began.
The Japanese invasion of Peking is referred to as taking place in 1941, but it actually took place in July, 1937.
When Prof. Burke is telling McGarrett about the history of Peking Man, he tells him the Japanese invaded China in 1941. However, it was in 1931 when Japan first invaded China.