When Wallaces wife is about to die, when he is running to the grove. You see he is holding no sword. But when he stops, suddenly he has a sword to throw in the ground!
This happens in another scene as well, when he is charging the English, first he is running with a sword, then without, the with again. WE decided that what happens to the sword is that he puts it in its case oh holder or whatever when he wants to...