I have some minor problems with it, and a close friend of mine had hers blown out.
The two most common symptoms i can think of are sleeping frequently, depending on how under active. My friend takes medicine, and if she goes 2-3 days without it she will fall asleep every 2-3 hours. But yours may not be as bad so may not be as strong.
The other symptom i know of is being cold. For some reason even medicine doesn't seem to do a lot to help this symptom. I remember once walking into her house, it was about 70-75 outside, nice warm day, and when i entered her house the wall of heat actually made me stop in my tracks. She was standing in front of the oven, with it turned on, apparently she had been there a while as her whole place felt like a steamer. I could barely breath it was so hot. Yet she leaned against the door of that stove saying how good it felt. Now its not always that bad. Now that i also have some thyroid issues i'm cold a lot. So be prepared to be colder than everyone around you and how you may need to dress.
Quick check on WebMD has this list..
-Feeling tired, weak or depressed
-Dry skin, brittle nails
-Cold
-Constipation
-Memory problems or trouble thinking clearly
-Heavy or irregular menstrual cycles
Assuming you don't have any of the symptoms hit very strong, and stay on the meds, its not a huge issue. Maybe just have your med levels tested once a year and watch for a flare up of symptoms in between. If symptoms flare just have it checked again. Hope this helped.