If your finch looks depressed, has odd colored diarrhea (yellow or bright green), and is losing weight or feathers, it just may have a protozoal infection. If untreated the finch could die. The color of the droppings and feather loss is probably the best indication of a protozoal infection. The only way to determine exact which protozoa are infecting your finch is to have a vet run a few cultures.
Protozoa can be passed from finch to finch fairly easily. Beak contact, contact with an infected birds droppings, or the feeding of chicks are all very common methods for the protozoa to travel to other finches in your flock. Once an infected individual is discovered you should separate it from the others as soon as possible. However because symptoms rarely show themselves until the finch has a rather severe infection it's very likely the other finches have also been exposed. It may be in your best interest to treat the entire flock at once.
The treatment I recommend is Ronex or Ronivet-S. Ronex/Ronivet-S is effective against motile protozoa such as Trichomonas, Hexamita, Giardia, and Cochlosoma in birds (budgies, pigeons, and canaries) suffering from canker (trichomoniasis) or other protozoal diseases eg. Cochlosoma in finches.
Ronivet-S is a water soluble, water stable chemical that has extremely high safety margins. It can be used at any stage of the birds breeding cycle to combat protozoal infection. Ronex does not make the male birds infertile.
Canker is the most commonly encountered protozoal disease in aviculture. It can devastate pigeon and budgie breeding flocks and is a significant disease in exhibition canaries. The classic "cankers " ( large yellowish masses in the throats and crops of birds ) are the "tip of the iceberg " when it comes to the disease. Many other effects are seen from Trichomonads.
Because protozoa are persistent organisms, treatments need to be part of an aviary/loft management plan. Preventative treatments are recommended to control the disease. New introductions and birds in quarantine should be routinely treated at recommended rates.
Resistance to antiprotozoal drugs is common. Unlike the other chemicals in its group, Ronidazole is safe to administer at up to 5 times recommended rate. In difficult situations treatment at 5X dose for 3 days then normal dose for 4 days has been found to be effective.