It is surprising that McGarrett and Five-O never knew of the presence of Miss Simpson, although they were watching Piro Manoa for a while and further had no idea that Chris Lahani was giving him information.
When they are reviewing the histories of the Five-O members on the computer, McGarrett's name is given as Stephen J. McGarrett. However, in a later episode, McGarrett says his middle name is Aloysius.
According to his birth certificate via the computer, McGarrett was born March 10, 1927. Something is erroneous with this date, since McGarrett describes himself later in the show as a Capricorn goat and stubborn. A birth date of March 10 would make him a Pisces.
When McGarrett shoots down the helicopter ( 1947 Bell 47D2, N47119) the burning wreckage flying though the sky is a plane and not a helicopter. Note this same helicopter was sometimes used as an HPD helicopter.
When McGarrett is shooting at the helicopter, he initially fires six shots that can be seen on camera. The fifth and sixth shots do not have the same muzzle-flash as the first four leading one to believe that the gun did not fire. However, the noise of a gun firing was heard.