In the "multiple dissection" scene, Tom Wilkinson uncovers each of the four dead bodies one at a time. But, following a quick edit to the applauding students, in a closer shot, one of the bodies is covered up again.
During Mad Maggie's hanging, the noose around her neck switches between tightness and looseness in each shot.
When the photographer takes the picture of the cadaver in Doctor Robert Knox's premises, he removes the glass plate from the camera and exposes it to (low level) light in the room. That action would have spoiled the photograph and an image is visible on the photographic plate. This would not have been seen.
Early in the film, Burke and Hare are shown to dig up a body to try to sell to Dr. Knox. In reality, there's no evidence that they were grave robbers, instead preferring to murder their victims in Hare's lodging house.
The "ex-Resurrectionist" in the pub says Dr Knox paid "three dollars" for a body. Dollars were not in use in Scotland; it should have been pounds (as indeed it was in the later negotiation between Burke & Hare and Knox).
Two hangings are shown in the film, in the style of a "long drop" designed to break the neck and cause instant death. This style was first introduced in the 1870s by William Marwood as a more humane approach. Before then, and certainly in 1828-1829 when the film was set, the victim was simply suspended by a rope around the neck and choked to death by suffocation.
Burke and Hare are in Greyfriars Churchyard, digging up a body, but are watched by a dog on John Gray's grave; this is presumably Greyfriars Bobby. In reality, Greyfriars Bobby lived around 1855-1872 so would have lived later than 1828/29 when the series of murders took place.
When Burke and Hare stop for a drink and Burke says that they have no money, Hare plucks a half-crown from underneath Burke's cap. The half-crown that is used in the film is from 1902-1910, which is nearly 100 years after the film is set.
The (Royal) Lyceum Theatre, referenced in the film, did not exist in 1828 as it was not built until 1883.
Hare comments that his wife Lucky has "fallen off the wagon" when she resumes drinking alcohol after a period of abstinence. The idiom of "falling off the wagon" would not be in used in Scotland at this time. The phrase originated in America very close to the start of the 20th century.