Walls and Ceilings - How do I repair previously poorly finished joints?

Our basement bathroom was put in by the previous owner. They did a poor job finishing all of the seams (esp. one floor to ceiling and one sink vanity to ceiling) as well as most nail holes. The seams/joints are not filled enough, and most of the edges in the room are not feathered enough.
I am wondering whether to finish what is there already or tear out the current drywall and install new (about 6 sheets). What do I need to do to prep the current walls so I can fill the joints better? Do I have to sand off the paint that's on there, to uncover the compound on the walls? What type of sander works best for this. I don't think that I can mud right over the painted wall joints.

Any ideas greatly appreciated.

Steve H.

You can put mud right over paint. Joint compound bonds to most surfaces very well. If the paint is a flat sheen then go right over it. If it is shiney you should rough it up with some sand paper first. Go around and tap on all the tape joints. If you hear any hallow sound then the tape is probably loose and needs to be cut away. Re tape as needed. Then determine if the joint needs to be filled or feathered out. Do this by taking a ten inch knife and hold it flat(blade edge to the wall). This acts as a straight edge and will reveal either a depresion or a bump. Finish as needed.