Should one always use the whole garlic clove? When using garlic cloves for pretty much anything, is it ever necessary to cut the slightly brown end off (that which connects to the head), or the middle out? Often times when I peel a garlic clove and cut into it I'll notice that the middle portion is slightly to moderately green and I'm always wondering if this should be discarded along with the brown end(s). If there are obvious blemishes in the garlic I'll remove those, but other than that is there a general rule of thumb?
The green in the center can have a bitter taste, and many chefs prefer to remove them. If the taste and color don't bother you, it will not cause problems for the dish. 

The brown end tends to a have a harder consistency than the rest of the clove, so may cause a problem depending on how you cook the garlic. If you're cooking it in a manner that leads to a very soft and mushy piece of garlic, you'd be better off discarding it. (Boiling in soup, for example.) It probably would not make much of a difference if you were browning the garlic for a topping.