While the best medicine is prevention, here are some common problems frogs are subject to.  If your pet frog is afflicted with an illness, the most important thing to do is to quarantine the frog before the illness spreads to other frogs in your collection.

• Nutritional Deficiencies:
  Caused by a lack of certain minerals or vitamins, this tends to show up in a variety of ways, such as skinniness and boneiness, and deformation diseases such as Rickets which cause poor growth development. Feed your frogs as much variety as possible, as this can occur mostly by feeding your frogs only one type of food: like nothing but mealworms, for example. In some cases, a routine application of powdered vitamin and mineral supplements will prevent such deficiencies. For example, feeding your crickets special powders/additives before feeding them to the frogs can help maintain more of a balance. The most common deficiency appears to be calcium. Sometimes frogs are picky about what sort of food they will take.  Sometimes you can coax frogs into eating by putting food on the ends of forceps (particularly if your dealing with some of the more aggressive frogs like Budgett's Frogs which can bite.  Be careful in choosing forceps that aren't sharp or you might end up with open wound illnesses instead of malnutrition illnesses!
   
• Wounds:
  Caused by handling, clumsiness (i.e. panic attack, smashing into or falling onto sharp objects), and fighting, such open wound and cut skin injuries tend to happen most to new specimens or during changing of environments. The wounds can easily get bacterial and fungal infections which can potentially kill your frog, so avoiding these situations is best. Badly damaged animals should be isolated and treated with anti-fungal solutions. There are a lot of anti-biotics available, and depending on the severity of the injury, treatment may consist of applying an iodine solution such as Betadine, or a commercial (3 percent) solution of Hydrogen Peroxide to the wound using a small paintbrush. However, the safest procedure is to consult a vet first.
   
• Red-leg:
  The most infamous frog disease of captive frogs, red-leg is usually caused by the parasite Aeromonas hydrophyla. It appears as a reddening of the skin, particularly on the belly and underside of the thighs, (not to be confused with the natural colorings of some species of frogs!) Frogs that get red-leg tend to act apathetic and lazy. This is a really lethal disease so isolate the affected frog(s) right away! Sometimes in the case of newly imported animals it is more likely due to abrasions caused by dry packing, like cardboard. In the latter case, the only treatment necessary is to correct the cause and keep the affected animal(s) in an incredibly clean cage for a few days. Otherwise, red-leg caught in it's early stages can sometimes be treated by bathing the frog in a Sulfamethiazine bath (15 ml for every 10 l water) daily for 2 weeks, or a 2% solution of copper sulfate or potassium permanganate for the same period. If it shows no signs of getting better after the first week, sometimes you can treat them with the use of an antibiotic like tetracycline, so consult your veterinarian on treatment.
   
• Fungal Infections:
  Particularly troublesome to the aquatic amphibians and tadpoles, this shows up as areas of red inflammation based on soft white tissue, though generally speaking, it looks like any noticeable abnormal changes in skin color might be a symptom of this. If caught in the early stages, a fungal infection can sometimes be treated by one of several methods: the most commonly recommended method is immersing the animal in a 2% solution of malachite green or mercurochrome for 5 minutes, repeating after 24 hours if symptoms do not improve. If no improvement shows after 3 such treatments seek the advise of a vet. Another treatment I ran across was coating with 8-hydroxyquinoline (one part per 5000 every other day) until the condition vanishes.
   
• Spring Disease:
  Caused by Bacterium ranicida, this lethal disease occurs in certain temperate species during breeding season. Symptoms include continuous yawning, lethargy and skin discoloration. Apparently, there isn't any reliable treatment for this disease, though experimentation with antibiotics may be worthwhile. Consult your vet.
   
• Dropsy:
  Possibly caused by bacteria, but much more likely a metabolism disorder - resulting from poor climactic maintenance or improper diet. Dropsy appears as bloating and soft dermal abnormalities around the abdominal region. The treatments sound really risky, involving puncturing the wounds if they aren't near the eye region.  It is strongly recommended that your frog see a specialist for treatment.