Sauron didn't actually see Luthien in his tower, because he was "wrapped in black thought". Interestingly enough, Tolkien makes a passing refference in Myths Transformed, that evil begets stupidity
Regarding Sauron in the movie, I found his depiction at the battle of the last alliance as distasteful. He was sweepping numenoreans and elves, when the books mention he was
forced to fight himself. And to go from that to have his hand
accidentally cut (not cut after being thrown down) is ridiculous.