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 1870's 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.
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.
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.