Captain Quinn states he's taking off in an F-94 Starfighter all weather interceptor, but the aircraft shown is a T-33 Shooting Star trainer.
In the epilogue describing the actual events depicted in this episode, the graphic which says "When Air Defense Command sent up two F-94 interceptors to investigate ...", it shows F-86 Sabre jets instead of F-94 Starfire aircraft.
The episode takes place in July, yet everyone wears heavy clothes and topcoats.
The General says that Truman will be gone in six months. He must be prescient, because elections are held in November and the President is sworn in January of the following year approximately two months later.
The scene at the Washington Monument outdoor field on July 19, 1952 shows two men tossing a Frisbee just before the alien orbs appeared in the sky. The Frisbee wasn't released until 1957.
Captain Quinn, in 1952, is riding a Vietnam-era Ford M151 "Mutt" Jeep, which didn't appear until ten years after this episode.
A young man is shown playing with a Frisbee which wasn't put on the market until 1964, twelve years later.
The US flags all had 50 stars. In 1952, the US flag had 48 stars.
Professor Hynek's contact gave him a five-digit street number for a meeting. Presumably that is a Washington, DC address since no city was named. Street numbers in Washington, DC only go up to four digits.