Continuity mistake: When Westley and Inigo are duelling, Westley flings his sword so that it sticks into the ground and then athletically flips from a bar to where the sword is and nonchalantly reaches down and back and takes it out of the ground. But if you watch, he lands too far away from the sword to do this.
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.
Continuity mistake: When Vizzini is cutting the rope at the top of the cliffs of insanity he cuts it really close to the rock the rope is wound around. In the following shots there is a lot of length of rope between the rock and where it was cut.
Continuity mistake: When Westley and Buttercup are walking through the Fire Swamp Westley's hair continually gets better or changes. One scene it is slicked back and another it is in his face or over to one side, etc.
Continuity mistake: When Fezzik falls to the ground after fighting with Westley, there is a very large rock right next to him. It is gone in the next shot.
Continuity mistake: There is a scene where Westley is matching wits with Vizzini. In every shot of Vizzini and Buttercup, her hair changes. In one shot, half of it is over her shoulder; in the next shot it is all down her back. This happens all through the scene.
Continuity mistake: Watch the red car behind Fred Savage in the bedroom. In close shots, the car is pointing towards the camera. In wide shots it's pointing sideways.