Factual error: Raymond is equipped with what is described as a high-power Soviet sniper rifle. However, the rifle he uses is actually a Japanese carbine.
Factual error: The movie is set in the mid 1950s, as established by the cars and 48-star American flag cake seen at the party scene. However, the convention hall at Madison Square Garden has 50-star American flags hanging from the ceiling.
Factual error: In the scene when the Senator and Raymond's mother are in the hotel room, the newspaper headline (upside down in the lower right) states that he will address the Senate that day. However, in the next scene when he proclaims there are 57 Communists (based on the Heinz ketchup), there is an uproar in the chamber and he yells "Point of order, Mr. Speaker." The Speaker (of the House) is not in the Senate, he is the head of the House of Representatives.
Answer: The shot in question occurs when Sinatra's character, Marco, holds up a deck full of queens while trying to deprogram Raymond. On the DVD commentary track, the director, Frankenheimer, acknowleges that the scene was out of focus, and that though Sinatra supplied several other takes of the scene, the other takes weren't nearly as good, so he went with the flawed one. Later, Frankenheimer was praised by critics for the unfocused shot showing Raymond's disturbed perceptions.