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.
After the woman with her son in her arms approaches the army in Odessa Steps sequence, she gets shot and falls backward with her son draped perpendicular across her. When the army marches down the steps after shooting the woman, the woman has turned 180 degrees around and her son is now lined up with her body.
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.
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.