I would say that any scope over 10X in power should have either the Adjustable Objective, or the side focus. I've seen some 4-12 scopes on the market without either and they have been hard to use for precise target work because of the parallax problem that would pop up at various ranges.
Fixed power scopes are adjusted for parallax at one yardage, usually about 150 yards. Once you get beyond that figure, the parallax gets worse and worse, but this is less noticeable/bothersome on lower power scopes.
Dan