In describing books,
my collectible first editions
would mean the earliest printing of the books, whereas
my first collectible editions
would mean the books that the speaker collected the earliest.
And it's not just because "first edition" is a technical term. "My horrible first year at college" is different from "My first horrible year at college" for the same reason.
EDIT: I've found another, quite different, and possibly better, example. Consider
poor unfortunate men
unfortunate poor men
(And if anybody thinks I cribbed this example from Disney's The Little Mermaid, they're completely correct.)
In the first, poor means pitiful and in the second, it means impoverished.
Why? I think it has to do with natural adjective order—in poor unfortunate men, the adjective poor is an opinion, which comes first in the order; while in unfortunate poor men, the adjective poor comes after unfortunate, so it has to be a quality (like unfortunate) and not an opinion.
The same thing happens, even less ambiguously, if you use tiny rather than unfortunate, because in the adjective order, size comes between opinion and quality. So in
poor tiny men
poor means pitiful, while in
tiny poor men
it means impoverished.