We spent a lot of time with Law in the manga, and still I've seen him OOC much more often than Kid. I think the most common mistake is having him too soft or too cruel.
It's true that Law is fundamentally a good character: he's not at all bloodthirsty, he fits in with the Strawhats and he prefers not to kill if he can, even his enemies. But he's everything except soft.
He cuts down people to pieces and walks away leaving them behind like that. He delivered a hundred beating hearts to the Marines.
Also, he's not emotional. He's pretty cold and collected. He does love his crew though, even if he doesn't always show it.
With his s/o. Law is the kind of guy that would only show affection in private and not in an overly amount. He'll always give his s/o the space they need to carry out their choices as independent individuals and he'll expect the same in return. He's teasing and sometimes trollish. He would be easily flustered, especially in public. Even if from a distance, he'll always keep an eye on his s/o to make sure they're fine. He wouldn't stress over a relationship easily.
He wouldn't fall for weakness, dumb people, cruel people.
