1. The Dud. Buy from someone you trust. If you lack close friends who raise goats, join your local goat club and make several. Do NOT buy a goat from a stranger.
2. Escapees. All goats want out. Two want out less than one, so buy two. Electric fences keep goats in but they will not keep dogs out.  Install good tight woven wire fences 4 1/2 feet high.
3. Dogs. A half-dozen miniature poodles can kill an adult goat if they gang up on her.  Do not let your own dogs out with your goats unsupervised.
4. Extra Baggage. Bucks and horns on your goats do not belong in the novice goatkeepers's herd, and the reasons are pretty apparent. The former are a lot of trouble, and the latter are dangerous. 
5. Biting Off More Than You Can Chew. It is a poor idea to practice on a milking doe. For your first goats, a couple of young doelings would be ideal. By the time they freshen you will have learned a lot about them. Take it slowly and do not let your enthusiasm get out of hand.
6. Illness. It can not be avoided entirely, but those who practice preventative medicine have less, and it is less serious when it does happen. Ask your veterinarian what vaccines and wormers he/she recommends, and ask some breeders about vitamin-mineral supplements, management tips, etc. If you start with good stock, vaccinate regularly, feed correctly, and are quick to notice changes in appearance and habits, and seek help, serious illness will be rare.
7. Economizing on Feed. Don't. Buy only the best hay you can get of a type recommended by people who raise dairy goats in your area, and feed as much as your does want. Stick to a grain formulated specifically for dairy goats. Find out how much grain to feed according to milk production needs. If you do not, your goats will be unhealthy and will not produce milk economically.
8. Lack of Preparation. Do not get caught short. Find out from experienced hands what you will need in the way of feeders, buckets, strainers, veterinary supplies, etc., and have it all ready before you need them.
9. Ignorance. It cannot be totally avoided. You can, however, get past the awkward novice stage rapidly and with a minimum of pain. Join your local goat club and go to all the meetings. Visit dairies and breeding farms and ask lots of questions. Go to shows. Get to know your veterinarian. Listen. Watch. Buy books and subscribe to magazines. How fast you learn is up to you.
10. Experimentation. Until you have had a lot if experience, leave this to wiser hands. A dairy animal is a very complex mechanism and the slightest error in feeding or management can have serious results. Just to give an example, both too-fat and the too-thin doe are susceptible to Ketosis, a very nasty disease that kills a lot of goats. Follow your vet's orders, and read all of the many fine books and magazines you are collecting.

Source:  Dairy Goat Handbook