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.
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.
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).
The actual battleship Potemkin was laid down in the Nikolaev, Ukraine shipyard in 1898, launched in 1900, and commissioned in 1903. After sailing unharmed through the Tsarist Black Sea Fleet as depicted in the movie, it sailed to Constanta, Romania where many of the mutinous crew remained. The Romanian government returned the Potemkin to Russia soon after.
The film was rejected for a UK cinema certificate in 1926 by the BBFC (British Board of Film Classification) following fears of working class insurrection, and it remained banned until January 1954 when it was finally released with an X certificate. This film was banned in the UK longer than any other film.