The flag seen flying on the ship after the crew had mutinied is white, which is the color of the tsars, but this was done so that it could be hand-painted red (the color of communism) on the celluloid. Since this is a black-and-white film, if the flag had been red it would have shown as black in the film. The flag was hand-tinted red for 108 frames by director Sergei Eisenstein for the film's premier.
The film censorship boards of several countries felt this movie would spread communism. France imposed a ban after a brief run in 1925; it lifted it in 1953 after the death of Russian leader Joseph Stalin. The UK banned it until 1954.
Konstantin Feldman, who played the part of the "student agitator," was actually a Menshevik activist in Odessa at the time of the mutiny and was present on the ship during the latter part of the mutiny. He died in the Stalinist purges of the 1930s (N. Bascom, "Red Mutiny" p. 294--although Bascom says Feldman played a sailor).
Acclaimed painter Francis Bacon considered this film a catalyst for his work, especially the infamous Odessa Steps sequence.
The famous Odessa steps sequence was not originally in the script but was devised during production.