Continuity mistake: During the first scene when the grandfather is reading to the grandson, he opens the book. When he gets his glasses the book is shut and he has to open it again.
Revealing mistake: In the duel between Inigo and Count Rugen, Inigo stabs the count in the right arm. But you can tell the sword is shorter, and it obviously wasn't stuck in the count's arm when he pulls it away.
Visible crew/equipment: In the duelling scene between Westley and Inigo, right after Westley has done his swinging on the bar and they go into the next shot, you can see Inigo jump up on a higher platform of rock, and then immediately after him, you can see Westley BOUNCE off the concealed trampoline onto the platform of rock.
Plot hole: In the scene where Westley is tortured to extremity, he screams, and upon hearing him scream, Inigo is instantly able to identify Westley and that he is in love with someone about to marry. You could say Fezzik told him, but how did Fezzik know? For all they knew, he was just a pirate after a prize.