Currently, as freelance I am cleaning up designs, props and even some backgrounds for My Gym Partner is a Monkey, airing on Cartoon Network. Before doing freelance for the show, I was the cleanup artist from 2005 - 2007 full time. The software I use for the cleanup is Flash MX.
I receive a rough and compose it for a sheet of paper, 8.5 x 11 on it's side. I then create a new layer, create a symbol on that layer, label the symbol the design name and then cleanup within that symbol. I also make sure to name the flash file the same name of the design that I am working . No doubt the production staff was happy about that. When I finish, I export the cleanup as an Illustrator file (.ai). Before I do, I make sure to turn the layer that contains the rough into a 'guide' layer. I never delete the rough because it's good to keep it there for any revisions or reviews.Generally, I will use a combination of techniques to cleanup a rough image. I will either use the brush tool and 'stroke' the line or if I cannot stroke the line cleanly, I will use the straight line tool using a line size appropriate for the volume. After I set the line, I will 'convert lines to fill' (which I have hot-keyed on my keyboard) and then use the black or while arrow to a just the line weight to give it the thick/thin feel. For revision purposes, I don't connect a lot of the cleanup lines that cross each other. I will 'group' lines that cross other lines which has two benefits. The first is that I can a just the line so as not to influence other lines I have stroked; that way keeping the integrity of my work. The second is at the tail end, if and when the cleanup needs a revision. The grouped line that is isolated is much easier to a just than a line that is connected and interlaced with other parts of the cleanup. Thus, revisions are quick, easy and relatively painless. (The only thing that gets bruised is my ego.)
The technique of cleanup for the show is a thick/thin line weight. However, there isn't a global use of thick on the outside, thin on the outside as is present in shows like Power Puff Girls. Instead the treatment of the line is to not only encase the border of the character, but to also handle the inside volume of the character. So a think outside line, will in some cases work it's way in to the volume of the character.
It's not a hard and fast rule that all lines on the outside are thick and the inside lines are thin. However, it is important that things like eyes and mouths, etc, don't become overly heavy with a black line. It is possible to go too thin for some interior lines that they become 'gossamer'.