Continuity: During the Odessa Steps sequence as the mother walks with her son towards the oncoming troops, a long shot shows as she approaches, the soldiers halt one flight of stairs above the one she is on. In the next shot, however, the soldiers are marching down another flight of stairs as if they are going to walk right past her. Then in the next scene they have stopped again and are on the same flight of stairs as if they hadn't moved at all.
Anachronisms: In the Imperial squadron near the end of the film, we see close-ups of triple gun turrets of Gangut-class dreadnought. It is possibly made this way to show the power of Imperial fleet, but this is an anachronism, for battleships of 1905 were much smaller pre-dreadnoughts, with twin turrets only, just like "Potemkin". "Ganguts" entered service in 1914.
Continuity: In the firing squad scene, just before the mutiny, the ship's priest taps a crucifix upon his right hand, holding it in his left. As the shot cuts to a close-up of the cross, it instantly switches hands.
Revealing mistakes: Vakulinchuk is breathing slightly as his body lies in state.