Removing mould from slides and negatives
First try to clean them without chemicals or liquids. Use a soft artist's brush to loosen debris and then blow the dirt off with compressed air. If that doesn't remove the mold then try plain water on a cotton swab.
It may be that you have a fungus that is living off the emulsion. If it is mold then a mild acid will likely soften it.
Try some white vinegar on a less important slide.
Other cleaning solutions are PEC-12, this does not eliminate any of the mold (it is indeed now part of the emulsion), but does get rid of other dust and grime.
Kodak recommend very pure Isopropyl alcohol but this can streak.
As a general rule be very careful in trying to remove mold by cleaning. Mold can eat into the emulsion and when you clean it you can pull away surrounding parts of it that were not covered by it.
You can scan your slides with digital ICE software which will get rid of a lot of dust and mould marks. If you don't have a scanner with ICE software, you can use Photoshop on the scanned images to remove marks. However, this can be quite laborious if the spotting is extensive.
Arrowfile can supply a scanner with digital ICE technology code M4000 by Braun.