I've been thinking about this nearly since dual spec is out. Would it be possible to:
List the two specs of the character (or say the second is empty if it's the case) on WoW-Heroes page (as the information is available on armory now)
Keep two sets of cached items, one for each spec (i.e. when the character is cached with spec 1 active, cache his equipment as "spec 1 gear", but if later he's updated with spec 2 active, cache that gear as "spec 2 gear"), then add an option to see gear cached for the unactive spec.
This would make things easier to check people on armory, as you might want them in your raid with the spec that is not currently cached either on wow-heroes or armory, but they might have been cached before (either from them querying or someone else querying when they were shown on their other spec on armory).
Of course for most people, the alternate spec might not be cached, and not up to date, but that can give an idea (if it's cached and good, we don't need to look further, if it isn't cached, well, that'll just be like it is now )