Corrected entry: The Scottish flag of a white cross on a navy background is used in the film but this flag was not used until later.
Corrected entry: In the movie, it seems like king Edward dies at the same time as Wallace. In reality, Edward I died in 1307, two years after Wallace.
Correction: Exactly - the movie only shows Edward I gravely ill. There's nothing in the film to suggest the king is dying as Wallace is being executed; rather he is suffering due to his illness.
Corrected entry: In the very first fight, Gibson had a flail and antlers. After he hits the 1st guy, he falls from his horse with flail in hand. When attacked by the 2nd guy, a sword is now in his hand and he blocks an attack with it.
Correction: Wallace drops the flail after he falls off the horse and picks up the sword of the first guard he killed.
Correction: This is probably the one bit of accurate history that Mel got right, and it was most likely an accident. In 909 A.D. the Scots prayed to St Columba for victory and bore his crozier before their army instead of a banner. This started a tradition, and 393 years later at the Battle of Roslin in 1302, this battle tradition was firmly in place and the Scots called on St Andrew, St Ninian and St Margaret, bearing their croziers before their army. Even at this early time, the crozier of St Andrew was a white diagonal cross on a blue background. Following this tradition, at Bannockburn, 1314, Robert the Bruce called on St Andrew again, using the same symbolism. The flag was not used to represent the country of Scotland though, confirming that which the previous submitter also mentions.