Other mistake: When Westley and Buttercup are in the fire swamp and Buttercup is burned for the first time look carefully at the fire spurt, it's several feet away from Buttercup and is clearly too far away to have burned her.
Other mistake: When Westley and Inigo are fighting, they are speaking very quickly to each other. They're talking about different fencing styles, and these styles actually exist. Just the same, their fencing has nothing to do with the styles.
Other mistake: When a disguised Westley see Vezzini holding a blindfolded Buttercup hostage, Vezzini is sitting down with a blanket, some food, two goblets and a bottle of wine. There's no way that Vezzini should have these as he wasn't carrying anything on him when he got out of the boat and Fezzik took everyone up the Cliffs of Insanity.
Answer: When Inigo was a child, Count Rugen came to Inigos father and requested a sword be made for him. When the sword was finished, Count Rugen refused to pay the price he originally offered for the sword. Inigos father refused to hand the sword over so Count Rugen killed Inigos father. Outraged, Inigo took the sword his father made and tried to kill Count Rugen. He has kept the sword ever since so he could use it to kill Count Rugen.