Usually a dog will appear thin and weak with a thyroid problem A simple blood test at the vet will determine if it has one and treatment is usually just a pill.
Common symptoms would be rapid weight loss (Or gain) depending on whether it is Hypo or hyper thyroiditis. Another symptom of progression would be bulging eyes as well as either extreme hyper activity or chronic fatigue. Either way this could progress into a more serious condition and should be properly diagnosed by a vet.
Thyroid issues with dogs can manifest in excessive shedding, lethargy, weight gain, slow heart rate, hyperpigmentation of the skin, anemia, and high cholesterol.