Aspect is the complement of point of view. As one changes one's point of view one sees a different aspect of what one is looking at. It is therefore natural that aspect should lead writers into the same traps as do point of view, viewpoint and standpoint. See POINT OF VIEW. It induces writers, through its vagueness, to prefer it to more precise words, and it lends itself to woolly circumlocution. I cannot believe that there was any clear conception in the head of the official who wrote "They must accept responsibility for the more fundamental aspects of the case". There is not the same obscurity about "the independence of the Teaching Hospitals is also of considerable importance from the aspect of finance", but the thought would have been more clearly expressed: "the independence of the Teaching Hospitals is also important financially".
Aspect is one of the words that should not be used without deliberation, and it should always be rejected if its only function is, as in the last example, to make a clumsy paraphrase of an adverb.