The flag seen flying on the ship after the crew had mutinied was white, which is the color of the tsars, but this was done so that it could be hand-painted red on the celluloid, which is the color of communism. Since this is a black-and-white film, if the flag had been red it would have shown up black in the film.
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 battleship used during the filming was not the "Knyaz Potyomkin-Tavricheskiy", but an older battleship called "Dvenadstat Apostolov" (The Twelve Apostles), as the original battleship 'Potyomkin' had been broken up in 1922.
The film was rejected for a UK cinema certificate in 1926 by the BBFC following fears of working class insurrection, and remained banned until January 1954 when it was finally released with an X certificate.
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 Tzarist 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.
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.)
Battleship "Dvenadtsat Apostolov", that played a part of "Potemkin", was in fact removed from active service in 1911 and served as a mine hulk until mid-1920s, when the film was made. Despite the fact that she was from a similar period (1892) and of similar size, she had to be heavily modified externally, first of all by addition of dummy gun turrets.
The ship that stands for battleship Potemkin, the Twelve Apostles, was beached in order to mark a sand bank, so the stern was deep into the rocks. That is the reason why, throughout the film, there are no panoramic shots of the ship, and the stern is never visible.
Battleship "Dvenadtsat Apostolov" actually was in the Imperial squadron, sent against "Potemkin". "Potemkin" itself was the newest and most powerful of Black Sea battleships, but Imperial forces were more numerous.
Cinematographer Eduard Tisse, who shot the famous Odessa steps massacre sequence, ironically used this location again the same year for a comic finale in Jewish Luck (1925) by director Solomon Mikhoels.
The movie was released in Moscow in 1925. It was competing for box office with Robin Hood (1922), an American movie starring Douglas Fairbanks. The Soviet government hoped that this film would earn more than "Robin Hood" in its opening week, as this would be a symbol of the "revitalization of Russia" arts after the Revolution. In any event, "Robin Hood" pulled in more money, but it was a close race.
On 4 November 2005, composer Yati Durant premiered a new score for large orchestra and quadraphonic electronics for the recently restored "Berlin" version of the movie, commissioned by the Cologne University of Music.
"Potemkin" changed name four times. The original full name was "Knyaz Potemkin-Tavricheskiy". As a result of the uprising, the government renamed her "Panteleymon" in 1905. In April of 1917 the ship returned to the name "Potemkin-Tavricheskiy" (without "Knyaz" - prince), but in May 1917 the name was changed to "Borets za svobodu" (the Freedom Fighter).
The trivia item below may give away important plot points.
The famous Odessa massacre on the steps never happened. It was presumably inserted by director Sergei M. Eisenstein for dramatic effect and to demonize the Imperial regime. This sequence was inspired by the Bloody Sunday massacre on January 22, 1905, almost five months before the mutiny on the Potemkin. The Imperial Russian Army opened fire on peaceful demonstrators outside the Winter Palace in Saint Petersburg. Approximately 1,000 people were killed or injured. This event was the catalyst of the failed Russian Revolution of 1905.