During the entire 51 days, David Koresh retains his mullet haircut. But there is historical archive footage, particularly after the FBI sent video cameras in to the Davidians, in which his hair is relatively short, like a butch cut or a crew cut.
The military vehicles are older models than those used in the actual siege. This was likely done because the U.S. military would not participate in filming, so the filmmakers had to rely on private collections.
Police are seen driving 1998 or later Ford Crown Victorias throughout the series.
The terrain around Mount Carmel is much too arid and treeless to pass for Central Texas in the spring. This is obvious when vintage footage of the actual raid is shown. The film set was built in the New Mexico desert near Santa Fe.