At the beginning of the movie, as the guard falls, he is wearing a large fluffy black hat, commonly known as a busby, which then appears and disappears in each subsequent shot.
In the beginning of the movie, when the Earth is shown, it's spinning in the wrong direction. (It could be the camera's motion which gives this impression rather than that of the Earth itself.)
The Russian name of Moscow Pravda is spelled wrong. The first letter should be the P from the Cyrillic alphabet, but is the Cyrillic L. The English letter D appears instead of the Cyrillic D (which resembles the Greek Delta.) In addition, in the headline they changed the P at the end of CCCP into the Cyrillic for P, forgetting that P is already the Cyrillic for R.