Late, but just in case this is useful, let me drop a few suggestions.
In addition to the great advice you've been given about cleaning the lining, don't forget to vacuum the inside! Also switch to the slender head attachment (don't know the name) to get in all the corners and crevices. I'm currently also rehabbing a JC rescued from the thrift store, but mine is a velour purse with leather. If it isn't too badly scuffed or dry, Apple conditioner might be enough help with the scuffs. If your bag has any lingering smells on the inside, I've found that putting little bags of potpourri inside the pursing, zipping it up and leaving it for a few days really helps - even with the JC velour. (My favorite potpourri is the one made with citrus!) Also, stubborn spots of dust/dirtiness that don't want to come out on the interior, you can try using a Q-tip to reach. In the case of the Juicy that I'm working on, I turned the bag partially inside out (not all the way because I was worried about bending the bottom), spot cleaned with diluted baby shampoo and gently rinsed out the shampoo by dabbing with a damp little towel. I first tried laundry detergent but it was difficult to work out of the cloth interior. Because I don't want to risk the glue running or getting product on the leather, I've been spot cleaning slowly, working my way across the interior of the bag, and I figure that - eventually - I'll have washed the whole inside. Although it is taking a while!
As for the exterior, to deal with spots on the leather, I first rubbed a q-tip slightly damp with water on the spots. Some of the marks had not actually penetrated the surface and came off easily. I then just dried off by dabbing gently with a little towel. For more troublesome marks, whateve's suggestions are more useful.