Mineral oil will definitely remove the dirt 
spots, but then you need to go through with soap 
& water to remove the oily residue left by the 
mineral oil.  This latter step is very annoying.  
If you accidentally get some on the paint, it's 
ok since it shouldn't remove paint.

A much riskier but easier method would be nail 
polish remover.  Nail polish remover can remove 
spots as well (not as much as mineral oil), but 
it will also remove paint.  So be very careful 
not to get any of it on the paint.  (unless you 
wanted to do it on purpose to get rid of stray 
paint marks)

For both methods above, I would use q-tips and 
have some paper towel ready just in case.

I would experiment on a cheap cel or a dirty 
transparency first before even attempting on the 
cel you want to fix up.

Oh, and if the cel is multilayer and has stuck 
layers, then you're in for one very long and 
frustrating night.  If there's a lot of adhesion 
between the stuck layers, then it probably won't 
be worth it to even attempt a clean up job.