Mason Skiles (Jon Hamm) warns that the operation may "go sideways." The movie is set in 1982 but this phrase wasn't commonly used until the early 2000's.
Several of the vehicles are from the wrong era, specifically a Cadillac limousine in the 1972 scenes, and a Jeep Wrangler in the 1982 scenes.
Alice returns to an apartment in which Cal has been staying that is said to be in a very unsafe area of the city. It is not realistic that a CIA operative in Beirut with responsibilities for supervising all Middle East operations would be domiciled in a very unsafe sector of any city in which his station was located.