Air New Zealand plane is a 737 when it leaves Fiji, but a 767 thereafter.
Gordon Vette was not an American, he was a New Zealander.
When Jay looks up and sees the 737 piloted by Gordon, the cockpit lights are full bright. Flying at night, and attempting to see an aircraft, the cockpit lights would be off. The usual night illumination in the cockpit comes from the instrument panel.
The plane Capt. Vette was flying was a DC-10, not a 737-200 (as showed taking off from Fiji) nor a 767 as shown throughout the movie. The DC-10 has 3 engines and both aircraft depicted on the movie are twin-engine.
When the sunset check is done by Jay in the aircraft and Auckland Center members outside the tower, they don't take into account the altitude/elevation of the aircraft and the ATC members. The aircraft appears to be less than than 100' above the water while the ATC members are at some undetermined height (looking from a railing part way up the control tower). Not checking beforehand could induce a significant error when the time was checked.