In the film, Elizabeth de Burgh is married to Robert the Bruce as a part of his submission to England in 1304. In reality, Robert and Elizabeth were married two years earlier having met at the English court.
In one scene it shows the priest facing the congregation , in those days the priest would say mass with his back to the congregation.
Although it may seem like the events of the film take place over a series of months, in actuality the time passed between the start of the film and the end is about three or four years.
Throughout the film, Bruce is referred to as "Your Majesty." The correct form of address for a Scottish monarch (and indeed an English monarch) at the time was "Your Grace." The title changed to "Your Majesty" in Scotland after the Acts of Union in 1707 (and in England in the early 16th century during Henry VIII's reign.)
A number of times the English army is seen leaving London over a bridge across a wide river, implying the River Thames. However, this would take the army south instead of to the north where Scotland actually lies.
The scene where Robert informs his brothers about the death of Wallace contains a shot of a heavily laden table prominently featuring an artichoke dish. Artichokes would not be introduced to the British Isles until 1530, by the Dutch - almost three centuries after the birth of Robert the Bruce.
Modern glass in the windows of the Douglas castle.
At the beginning, during the outdoor celebrations, there's a sword fight. A page comes running up yelling "Your majesty" four times. Twice while off-camera, and twice when he comes into the scene, but for these last two times, his lips are not moving.
Despite sporting graying hair and looking to be in his 40s, Robert would've actually been in his late 20s and early 30s during the events of the film.
Elizabeth looks mortified and afraid when the guests of the wedding feast start making suggestion about the wedding night. In reality, a woman of the age would have been quite familiar with those procedures, as the public bedding of noble newlyweds was quite common. The notion of marriage for love is a modern one, and at the time it would have been seen as a contract, and women were educated to expect it.