Is eating only boiled foods unhealthy? If everything I eat is boiled, will I develop a deficiency? What will I miss by not trying other cooking methods?
You will miss nothing, except maybe some texture and some enzymes.
The Bulletproof diet suggests gentle cooking of all foods, and broths with boiled meats are extremely easy to digest. You might want to eat some raw foods for good enzymes, but for most of history, meat was cooked in stews.
I wouldn't say it's unhealthy. Eating McDonalds at every meal is probably 'unhealthy'.
Certain vitamins and mnerals can leech into the liquid though (and oxalates too, which many don't really want anyway). If you're not consuming that liquid you may miss something. And enzymes and possible enjoyment/reward, like other posters have mentioned (roast meat/veg anyone?)
On a positve, by boiling meat you will 'miss' the hetrocyclic amines that form through high-heat cooking, which may be harmful... http://www.cancer.gov/cancertopics/factsheet/Risk/cooked-meats
You are certainly not unhealthy by boiling all the time. If you're like me though you may desire addiational variety/less rigidity after getting bored with constant concumpsion of boiledstewed stuff.*
nb There is nothing I like more than low and slow braised lamb or beef...
The concern with boiled foods is that nutrients, especially minerals end up in the water. If you boil foods, and keep the water to drink or as a gravy/ broth/ etc then you will lose nothing nutritionally.
The other concern is with texture. if this is not an issue for you, then boil away!