When Jack is chasing the sniper, the sniper is shown running through an alley way with two adults and a child in front of him. After climbing onto the roof, jumping off, and climbing a couple of walls...he is shown again in the same scene running through the alley with the same three people there.
When the British soldiers, led by Lt. Durrance, are chasing the sniper in the village, one of the British soldiers shoots two rounds in rapid succession at the fleeing sniper, which is impossible with the Martini-Henry rifles with which they were armed. Martini-Henrys are single-shot rifles.
British forces fighting in the Omdurman campaign of 1898 wore khaki uniforms, not the scarlet jackets used in this film. However even while earlier British infantry soldiers did wear red coats, the cavalry of that period wore blue jackets. The scene in which Dervish horsemen impersonate British cavalry wearing red jackets would be historically inaccurate for both periods.
When they arrive at the fort at 58.05 the flag, the Union Flag has been flipped so that the red diagonal St Patricks Cross is on the lower half of the white diagonal St Andrews Cross on the lower right of the flag when it should be on the upper half of the white diagonal on the lower right.
At 52.30 when the British soldier fires at the guys escaping on camels, he also fires two shots without reloading in between. Again this would have been impossible with the Martini-Henry rifles as they are single shot breech-loaders (as seen famously in 'Zulu' and 'Zulu Dawn').
In the opening rugby match sequence at least three violent fouls (including what appears to be someone having his nose broken) occur before the referee blows his whistle. Even in a physical sport like rugby this wouldn't happen at an organized competition.
When Harry loses his horse and has to jump onto the back of a free one, you can see the rider next to it holding its reins so it will keep running. There is no reason for him to be doing this in the middle of a charge, except to have it ready for Harry to mount.