There is one thing I absolutely love to do with PoV characters, and that's to have them contradict each other. Neither characters are lying, but their respective perspective on life reflects on how they narrate the story. There's a few ways this can become apparent.
1. Their opinion about others. Two characters can have wildly different opinions about the same third character. Say this third man is a king. The courtier who has just been awarded bigger lands may love this king, and describe him as just and generous. The king's wife, whom he hits in a bout of anger, will disagree with that. Or the people dying of hunger in the streets while he holds banquets might not be so keen on calling him 'generous'.
2. Their opinion about each other. This one is even funnier, if you ask me. A relationship isn't always equal on both sides. One character will not always reciprocate the other's feelings.
I just read a perfect example of this is Guy Gavriel Kay's A Song for Arbonne. The chancellor is madly in love with the countess, Signe. He knows it is an impossible relationship, and he has a wife and kids, but he considers this eternal love a simple fact of his life. Signe, however, has no clues about this love. She wonders at times what the chancellor thinks of her and concludes he must believe her weak, and in need of support.
This is fun. It's fun to read and it's fun to write. It's also quite realistic. Not everyone I consider a close friend thinks the same of me, and vice-versa. I often read about this kind of diverging opinions with unrequited love subplots, but it's not limited to it! Go wild.
3. Their versions of events. Two different POVs can tell the very same scene in completely different ways. What a rebel leader thinks of an oppressing government's fall is quite different to how this government's leader will feel about it. Pick any two characters in a scene, and they should have different opinion on what's going on.
There's nothing like contradicting PoVs to add some shades of grey to characters and worlds. You don't have to visit everyone's head to do this. Two characters with different backgrounds are more than enough to bring out the "contradictions" in your story and in your world.