Alan tells Charlie that the space program gave us Velcro and Tang. It did neither. Tang was invented as a breakfast drink and became popular when NASA began using. Velcro was invented in 1941, well before the space program. Velcro was blamed for the severity of the Apollo 1 fire (not the cause).
Velcro was conceived in 1941, invented later on in the decade, with a patent request sent in 1951, and approved in 1955.
Twice Charlie uses the letters S-G-S, when referring to the Scientific Jury Selection program. Later he correctly identifies it as S-J-S.
When Charles Eppes is explaining his Spacial Dynamic Jury Model, he uses the metaphor of a coin flip. The coin shown flipping is a Morgan Silver Dollar. As the coin flips end-over-end, you see an upside down eagle, but in reality the eagle would be right side up when flipping end over end.