Continuity mistake: About 30 minutes away from the end, Brother Belcher can be seen walking past the gates. Then, when he's 1 yard away from the gates just to make sure it's all clear for him to go, he gets a bullet that flies out of nowhere. When the bullet hits his hat, the hat shoots upward and out of shot. In the wide shot of all the gates and the walls, there is no sign of his hat.
Other mistake: The fight at the end is unintentionally quite funny for the lack of enthusiasm shown by the extras playing the Burpers. They engage the British soldiers with some half-hearted fighting that's little more than jostling, and when they disengage the fight supposedly in fear and panic at seeing the "Men in Skirts" reveal themselves, most of them are quite slow and calm as they try and get through the narrow gate to escape.
Continuity mistake: As the fake chiefs escape over a wall in the palace, the door they locked is shown being battered down by Burpers. From the inside shot it takes noticeable damage, and begins to come away from the wall on the hinged side. However, when the fakir opens it from the other side everything is now fixed, and it opens just fine, no signs of damage.
Continuity mistake: When Brother Belcher is horrified to see the Fakir's head being served during the dinner sequence, the dust stains on the shoulders of his dinner jacket change between shots.
Continuity mistake: When Bungdit Din yells "Fire!" to commence the attack on the palace, he is holding his sword in his right hand. In the next shot, he is holding the sword with both hands.
Continuity mistake: Lady Ruff-Diamond is covered in plaster during the dinner sequence, but when we see her drinking her glass of wine with the others, she is spotlessly clean.
Continuity mistake: During the dinner party sequence, a bullet strikes the wine bottle that Sir Sidney is holding and his dinner jacket shirt is covered in red wine. When the orchestra stop playing, we cut to Sir Sidney and his shirt is spotlessly clean.
Continuity mistake: Brother Belcher is shown ducking under the water line in the fountain when he and the others are revealed as the fake chiefs. When the shot cuts to the side, he is above the water line again but now completely wet. Then the shot cuts to the front again and he is shown coming up from below the waterline.
Factual error: The revolvers carried and used by Sir Sidney Ruff-Diamond, Captain Keene and Sergeant Major Mcnutt throughout the film (and particularly at the end fight) are Webley MkVI's, not introduced into the British Army until 1915, 20 years after the film is set. Additionally, the holsters Keene and Mcnutt carry them in are webbing holsters, not introduced until well after WW1 (1914-1919).
Factual error: After finding the soldiers slaughtered at the Khyber Pass, Sergeant Major Mcnutt and Private Widdle try to see off the Burpers with a "Maxim". The Maxims in use at this time look nothing like the gun they use, which appears to be loosely based on a Gatling gun. Additionally, it's mounted on a MkIV tripod, not introduced to the British Army until 1906, 11 years after the film is set.