Good question. As with all first-aid products, it's important to prevent access to products, carefully monitoring the dog and keeping such products out of the way. Dogs should also be discouraged from licking off products either through careful supervision, distraction or the use of an Elizabethan cover when close supervision or redirection isn't possible.
According to veterinarian Dr. Andy, in general, ingesting a very small amount of diluted betadine shouldn't be a concern for toxicity. Some dogs with very sensitive stomachs though may develop some mild gastrointestinal irritation (nausea, vomiting, and possibly diarrhea). Large quantities are more problematic. Veterinarian Dr. Kara mentions that excess iodine can be toxic to a dog's thyroid gland causing electrolyte disturbances, but in general, a few licks should not be a problem. Encouraging the dog to drink may be helpful. Ice cubes, fresh water or low sodium broth with no onion or garlic in it can help. A dog who acts sick or ingests a larger amount should report to their vets or poison control.