The whole space station doesn't need to rotate in order to create artificial gravity. Just keep the living quarters in the rotating bit and the experiment areas in the none rotating bit.
It's not that simple. If you're rotating on a small radius, you're going to have a noticeable difference in apparent gravity between your feet and your head. Just as we don't know what long duration low gravity does to the human body, we don't know what long duration tidal gravity will do. If you're rotating on a large radius, well now you've got to construct this huge, high strength station. Now obviously, the only way we're ever going to find out is to throw something into orbit, and spend several years manning the thing, but the problem is a complex and not well understood one.
The hard part is probably trying to keep one area stationary while the other rotates. That's going to require something rotating in the opposite direction to cancel out any momentum.
Why do you have to cancel out any momentum? Why can the station not have a non-zero rotational momentum? Tons of satellites do.