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.
Continuity mistake: After Montoya has hauled Wesley to the top of the cliff, he drops the rope on the ground, where it lands forming a couple of coils. You can see this as Wesley sits down and Montoya leans up against the wall. However, when they start their duel, the rope is hanging straight off the cliff, without any coils in it.
Revealing mistake: When Fezzik is about to climb the rope going up the Cliffs of Insanity with Inigo, Vizzini and Buttercup all harnessed to him, Buttercup is the most visibly seen (besides Fezzik) in the camera. When Fezzik starts to ascend the rope, it is clearly obvious that Buttercup is a stuffed dummy because her head is flopped completely back.
Continuity mistake: After the grandfather has finished reading the book, he stands up to put on his hat and coat. The shot goes to behind him, and we see that he has already put his left arm through the sleeve. Then the shot changes again and we see him from the front as he is sliding his left arm into the sleeve.
Continuity mistake: When Inigo and Count Rugen are duelling in the banquet room, watch the Count's sword: after he stabs Inigo near each shoulder and draws out the sword it is clean. A moment later, as Inigo falls forward a bit and then rights himself, blood is seen on the Count's sword. If you watch both their swords during this entire scene you'll see the disappearing/reappearing blood.
Visible crew/equipment: There is a scene where the Prince and the Count are talking at the entrance of The Pit of Despair and the sound mike can be seen bobbing around on top. [This is only visible in the original 1980s VHS pan-and-scan version of the film, and is due to the open-matte process that was used to produce the VHS release. See http://www.widescreen.org/widescreen_matte.shtml for an illustration. Still a mistake, but there's why - pan and scan is evil.]
Continuity mistake: When Fezzik falls to the ground after fighting with Westley, there is a very large rock right next to him. However, when Westley tries to roll over Fezzik, the large rock is too close to do so. Therefore, the next shot shows them further away from the rock so Fezzik can be rolled over.