In the opening scene where Steve is riding with the Governor in his Lincoln Continental sedan, this 3-minute ride starts out in a 1970 Lincoln, continues in a 1972 model, and finishes up in a 1971.
The plane used by the terrorists arrived at the airport at 5:00 PM. Some time later, after the terrorists' plot is foiled, when McGarrett is talking to Dr. Haig, a large clock tower can be seen over McGarrett's shoulder and the time on it is about 1:25 PM.
The character pointing gun at Danno as the money is being transferred at the end is not wearing sunglasses. But in the last shot before he boards the plane, he is wearing them.
When Dr. Haig tests the plutonium sample, he uses a standard Geiger counter. The Geiger counter only detects Beta and Gamma radiation. Plutonium is an Alpha particle emitter. Alpha particles would be blocked by the plastic case. To confirm the material is weapons grade plutonium would require the use of a mass spectrometer.
Uranium-235 is shown labeled on propane cylinders, while polonium-210 is shown labeled on gas cylinders; such isotopes are neither liquid nor solid and cannot be kept in such containers as these.
When Kapiolani Park is being evacuated, the firetruck is shown with Ala Wai Canal on its right. If the firetruck is heading is heading toward Kapiolani Park, the canal should be on it's left. The firetruck is heading out of Waikiki and away from Kapiolani Park.
The HPD helicopter evacuating the park was a Hughes 369, it is a turbine engine helicopter-4 bladed. The sound was not correct, it was that of a Bell 47 or similar piston engine helicopter-2 bladed.
The fire from the explosion of the plane shot by HPD to stop it didn't match the motion of the plane, it was superimposed. The wreckage shown afterward did not resemble the plane that was shot down.
Danno, flying in a helicopter and speaking through a megaphone, clears the park area. But the people only run to the park's outer boundaries.
As Dr. Haig is taken to the ambulance McGarrett seems to give him a pass for his assist in neutralizing the bomb, as he is not charged with conspiracy in the extortion scheme.
After the doctor goes into the bathroom to diffuse the bomb, McGarrett is told by an expert that if the bomb explodes the facility will have to be isolated for months due to radioactivity. Then the bomb explodes and McGarret and several officers run toward the building. The exact opposite of what the expert just said.
When several jurisdictions of law enforcement went to Kapiolani Park to dismantle the device that would produce an atomic flash, they failed to wear adequate protective gear. When Dr. Haig wheels the vendor's cart containing the device into the lavatory, he is completely unprotected. The HPD bomb squad, working with federal authorities, should have ensured that everyone involved was properly protected against radiation poisoning.