It sounds like a bacterial infection of some kind like columnaris.
Here read this excerpt from another forum. Columnaris
Grayish white marks or patches on the body of the fish or around its mouth are the first obvious signs of Columnaris. These patches appear like threads, especially in the vicinity of the mouth. Hence, this is often confused with another disease called "Mouth [COLOR=black! important][COLOR=black! important]Fungus[/color][/color]
". The fins of the fish may show signs of deterioration, the gills get affected and slowly sores start appearing on the body. During a later stage the fish can hold its fins very close to the body and not spreading them. Columnaris disease is caused by bacteria, and is mostly a direct result of poor water quality. Sometimes, the shock of being introduced to the new aquarium leads to Columnaris disease in newly imported fish. Anti-bacterial medications will be enough if the disease is discovered and treated at its early stages. The disease will however invade the internal organs during the later stages and antibiotics are then required to cure it.
What I think you are seeing is the end stages of the columanaris but treatment is available. You need antibotics for this like Maracyn or Maracyn 2. Also Tetracycline is a good med for this.
But mainly you need to check your water parameters and you might need to do more frequent Water changes.