The Arrow was canceled in February 1959, yet when the existing aircraft and all plans, blueprints and models are ordered destroyed, we see a model of the final design of the Apollo Lunar Module being collected from one of the offices. The contract for the Lunar Module was not awarded to the Grumman Aircraft Engineering Corporation until mid-1962 and did not reach its final design until 1965 so it is not possible that a model of this final design would be available in 1959.
When Jack Woodman and Air Marshall Curtis are informed by a cabinet minister that the United States will protect Canada until the Bomarc Missles are operational, Woodman stands up and states that Canada should just sit back and become the "49th state", even though you can see he says, "50th state."
In the movie the engines were silent when the sound barrier was broken. When one breaks the sound barrier, the engines do not all of a sudden become quiet. The sound can be heard through the aircraft itself.
Jim Chamberlain is depicted, in 1957, as having discovered the area-rule or "coke-bottle" shape for reducing compressibility during trans-sonic flight. The concept was in fact discovered by Richard Whitcomb at the Langely Research Center for which he received the 1954 Collier Award. The technical details were made public in 1955 and the F-102, F-104 and F-105 were already in service with this design. The wind-tunnel at Langely was able to allow Mach 2 testing of the Arrow because it too was using an area rule cross-section.