yogurt is a fermented milk product and generally tolerated very well by all dogs.
the kind made from whole milk is nutritionally the most valuable, but fat free or low fat is fine too.
the issue about digestion isn't about casein, but about lactose, which is a problem where dogs (or people) who are lactose intolerant ingest large amounts. during fermentation by bacteria, much of the lactose in yogurt is converted already tho.
the live cultures are excellent for supporting the digestive tract and immune system. more info here:
http://www.mordanna.com/dogfood/index.php?page=probiotics
plain yogurt is generally recommended since sweeteners/sugars are something dogs definitely don't need in their diet. it's not so much about issues with flavorings etc., just a common sense thing.