The Appropriateness of Adjectival Nouns

Ok, so this is probably a slightly different subject from what many of my other posts will be, but I'm a huge linguistics nerd too, so I thought I'd kick it off with this, based on a discussion a few of us had a couple weeks ago.

So here's the main question: Is calling someone an "[adjective]" as a noun versus an "[adjective] person," inherently offensive labeling, or is this usage somewhat an accident of language? For example, we can all pretty much agree that calling someone a "schizophrenic" versus "a schizophrenic person" or "person with schizophrenia," is offensive, but is it always the case?