In the depiction of the Battle of Omdurman, the film states the famous charge of the 21st Lancers, which included Winston Churchill, happened the next day "during mopping up operations". In fact the charge happened on the same day as the main battle.
When the British artillery is laying waste to the Mahdist charge at Omdurman, several of the extras are obviously running in place so as not to accidentally be near where the explosives detonate.
When Lady Churchill is first seen playing the piano (whilst being interviewed by an unseen person) the notes we hear do not correspond with her striking the keys on the keyboard.
Just as 'the last ever cavalry charge' is starting, there's a 'cavalry-mans view' towards the enemy lines. The wheel marks of the vehicle carrying the camera are visible, presumably from previous takes.
As the 'last ever cavalry charge' reached the enemy lines, a white flare, used as a signal for the hordes of extras, can be seen dropping from the sky.