Character mistake: When Melanie and Scarlett are talking with an (off-screen) wounded Confederate soldier, the soldier says he hasn't heard from his brother since Bull Run. Only Northerners refer to that battle as Bull Run; Southerners have always referred to it as Manassas.
Revealing mistake: When they are feeding Annie the Elephant medicine with a wooden spoon, there is obviously no fluid in the spoon.
Factual error: Towards the beginning of the film, when Kitchener is shown inspecting Harry's old regiment, one of the African or Egyptian troops is shown to be wearing the Pattern 1914 Infantry Equipment, not made until 1914 at the earliest. Additionally, it has the 1918 modification to have two closing straps, so is over 20 years too late for the 1894 date at that point.
Other mistake: Just after newlyweds Gil and Lana arrive at Gil's small log cabin, they are visited by a Native American named Blue Back, who brings them a side of venison. Even though it has been pouring rain outside for hours, Blue Back is perfectly dry when he enters the cabin.