See completion of an area while not in the neighborhood?
Solution 1:
Fortunately, yes!
As of the Wintersday '12 patch, it is possible to see your completion on zones 'at a glance', simply by hovering your cursor over the region in question.
This is also present on the individual zone loading screens.
Solution 2:
Unfortunately, no.
In the initial release, there was no way of knowing which zones had partial/full completion, or even what the progress was in any zone other than the one you were in.
The only way to know for sure was to go into each zone and check.
However, as of a recent update, the game allows you to see your progress by mousing over the zone name on your map.