1. The film opens with Ed Gein killing his brother,Henry with a shovel in 1944; actually, the police investigated Henry Gein's death at the time and found no evidence of foul play- and the official coroner's report states that Henry Gein died of asphyxiation while fighting a fire on his property. While many authors have suggested that Ed murdered his brother (especially after the revelations of Ed's later activities) this has never been proven.
2. At one point, when talking to his secretary, Hitchcock (Anthony Hopkins) refers to Ed Gein as "the mass murderer from Wisconsin". In reality, there were only two confirmed murder victims of Ed Gein, which, although terrible, hardly constitutes a "mass".
Finally, in the same conversation, Hitchcock refers to Gein as "the boy who dug up his own mother". Although Ed Gein was a proven grave robber- which was and is a terrible crime- there is nothing in historical records of his crimes mentioning- or even suggesting- that he exhumed his own mother's remains.