Mouth Fungus is a contagious goldfish illness, also called Chondrococcus. It is actually a bacterial infection caused by flexibacter.
Symptoms: White cottony appearing growth on mouth. It can then extend to the gills, back and fins. If untreated will lead to the destruction of the mouth and possible death.
Treatment: Commercial cures are available at your local or online pet store. Isolate your infected fish and disinfect your tank. It is recommended your treatment be a broad spectrum antibiotic and anti-fungal combined therapy.
If you are unable to get treatment medications immediately then place your effected fish in a salt bath.