What brand of strings are you using??? I've only changed one nut on a Gibson, which was my BluesHawk. I went with bone just because that's what my taste gears me towards. But I would check the bridge and the tuners first before I would put a new nut on.
If your tuners are really easy to turn then that is most likely your problem. I know that's how it is with my SG Standard, the tuners are so loose that if I bend a step up it goes right out of tune.