The fake driver's license they prepare for Friday shows him to be born in 1925 and has an issue date of 1964, which would make him 39 at the time the license was issued. However, the age printed in the license is 42, which is what his age would be at the time of airing in 1967.
When Friday gets his first instructions on the phone from the man who placed the ad, he listens for 3 seconds. When he tells Gannon what the instructions were, it takes him about 12 seconds to repeat the very complex message. He could never have heard all that in the 3 seconds on the phone.
As Sergeant Friday is driving the 1960 Ford station wagon in the middle of the night, you can clearly see that the transmission lever is still in its "Park" position.