Let me start by showing you something that you cannot clean:
There is no known way to remove red fade, and collector's have tried bleach and every cleaning agent known to man. It appears to be a permanent condition. So keep your red figures separate if you store them in big mounds like I used to.
Now on to what can be cleaned: dirt and assorted filth.
I think all of us have received filthy figures in the mail, particularly from Ebay sellers. Especially true for Argentina MIMP (for reasons I cannot answer).
It is much easier to clean the monocolor figures. They can be cleaned with rubbing alcohol or simple soap and water. You can also add a small amount of bleach in the water if the figures are especially dirty. But don't put too much or you might cause the colors to become dull.
A special note: DO NOT USE RUBBING ALCOHOL on the Hardee's Dinosaurs! For some reason they seem more susceptible to fading.
The painted figures bring a special complication:
That is about all I have to say about cleaning MIMP. Feel free to share any methods you use or have used below and thanks for reading!
EDIT: Thanks again to James Roth for suggesting this week's blog topic.