I am scanning my fathers slides that got damaged last year in a move. They have been in slide magazines (Airequipt) for years. Moving day, last year, the moving boxes they were in had gotten wet. I did not know until recently, when I opened my guest room closet where I had the movers stack the boxes and was bowled over by the musty smell. I drug all the boxes out to the garage and tore off the cardboard Airequipt boxes that were notably damaged, after photographing the labeling on each end box. I bought archival boxes to store the slides in after I finish scanning them. In the meantime, as I am scanning, I am separating the damaged, no image slides, into zip lock bags and putting all scanned slides into lidded plastic tubs with a bowl of activated charcoal in each, to store until no noticeable smell remains. My question is: if there is any mold in with the scanned slides will it continue to deteriorate the good slides when archived? Typically my house is between 72-77 degrees and humidity ranges between 40-51 percent.
If the slides are mounted in cardboard frames, you'll need to replace the frames, since they will contain mold spores, as well as clean the film with isopropyl alcohol, as @Peter_Taylor mentioned. There is a nice tutorial for the entire process on WikiHow.
If the mould previously found something to digest in the slides (probably gelatin) then there's no reason it should stop unless you sterilise it. The best sterilising solution may depend on the film stock used. Kodak recommends dry (i.e. minimal water content) isopropyl alcohol.