Nietzsche is very widely misunderstood about some of his central viewpoints. He's associated with Schopenhauer's pessimistic (depressed) outlook, and not without reason. One of his early works is an admiring take on Schopenhauer. But he rejected that pessimism outlook in the most emphatic way imaginable, even while suffering health problems which might have left many people very depressed.
Another reason why Nietzsche is often misunderstood is because his most popular book, Also Sprach Zarathustra,is written entirely in mostly-cryptic verse, and people have tended to see whatever they want to see in it, the way children see duckies and horsies in puffy white clouds. (He wrote once, in reference to Wagner,that artists often don't know what they themselves do best, because they're too vain to see their own work for what it is. I think this ironically applies to Nietzsche himself. He called Zarathustra his best book. I think his best work is his prose, especially when he's being very direct.)
Then there's the perception that Nietzsche was antisemitic. Not true. However, his brother-in-law led an antisemitic political movement, and his sister did all she could to associate his name with that movement, despite his vehement objections. Also, Richard Wagner, Nietzsche's mentor for a while, to whom Die Geburt der Tragödieis downright gushingly dedicated, was antisemitic -- or, in Nietzsche's account of things, let himself be associated with anti-semites. (Whom Nietzsche referred to as the lowest of the low. How much more clear could he have been?) (And Schopenhauer was antisemitic too.)
It's true that Nietzsche was stupidly sexist, though. In his published works, whenever he mentions women, that brilliant mind just gets shut off. He rarely mentions any individual women, just refers to "die Frau" as such, or, oftener, "das Weib," which is a slightly less respectful way of referring to women. After knowing only his philosophical works, it was quite a surprise for me to read some of his lettersand find him writing to and about individual women in a civilized and friendly way. (Even more surprising that they wrote back, if they'd read his books. He must have been very charming indeed.)