I am affraid the moisture have already taken it's toll and all over the movement too.
I would have taken and do now, take the watch to service centers. Moisture ruins lubricants.
In general, as soon as the moisture appears, the dial should be dealt with. Placing the watch under direct sun light or expose to other very mild heat, also taking the movement out to submerge in lighter fluid and blow dry helps reduce the damage, before you urgently get the watch to service man.
There are some treatment to somewhat clean the dial. Depending on the value of the watch, the job should be entrusted solely to professionals. Do not attepmt yourself.
Regards joe