When cycling, Prof. Jones is nearly run-over by a reversing light coloured sedan. An immediate cut to a left angle camera shows a two tone station wagon.
At the tennis court, the same group of people walk behind Prof. Jones twice.
When John and Virginia are trying to find Donna and Jimmy, there is a white car with black metal stripes in front right behind Jimmy's car. But the exact same car is also seen right behind Virginia's car.
At the end of the movie when various newspapers tell the story about the "Zotz"-Coin a Soviet Newspaper is shown. While the main headline is written correctly in modern Russian, the other smaller headlines are written with the "Yat"-sign at the end of every word. While this character (now known as "Hard sign") still exists, writing it at the end of almost every word wasn't in use until the late 1910s and was not done in the 1960s when the movie came out (and is still not).
When Professor Jones is being given directions, the officer tells him that the five sides of the Pentagon building are lettered A through E. This is not correct. The letter designations are given to the five pentagonal "rings", with A the innermost and E the outermost. Ten numbered corridors connect the rings. Offices are designated by floor number, ring letter, corridor and room number, e.g., 4C515, a system that is far less complicated than the one being explained.
The views outside of the General's office at the Pentagon are completely wrong. The Pentagon is located to the west of the Potomac River. The Capitol is miles to the East. In the General's office window it appears that the Capitol is just down the block. The Pentagon is not tall, being (about five or six stories) the views show the General's office looking DOWN on several other multi-story Government buildings. The views from the Pentagon are parking lots and the Potomac River.