When Henry and Molly are driving back from Massachusetts, they pass the same scenery over and over again, that scenery stock rear projection.
The car Henry and Molly take to Massachusetts is shown with not one, but two radio telephones. However, the car does not have any large external antennas, which would have been required at the time - well before cellular and satellite phones. Also note that the review mirror and sun visors that would be normally attached to the windshield frame have been removed.
When the Texas oilmen find out that Henry is in New York, they tell the pilot to head to New York. The plane turns and banks and the flag in the plane leans to the right (pointing towards the ground. BUT the flag should have continued to hang straight down toward the floor as centrifugal force would flung the flag outward instead of downward.
(at around 5 mins) When the old lady, who steals the cab from Henry, closes the door, a cameraman, camera, tripod, and microphone are all reflected clearly.