* Starting in "The Emissary", we see a map of the galaxy showing territory explored. (The map is seen to the right of Worf in this image - http://tng.trekcore.com/gallery/albu...missary098.jpg
) The area covered seems more than the 19,000 light years (19% of the MWG) that Wesley said that the Federation had explored by then.
This particular image does't bother me... After all, 19% is nearly 1/5, and that image looks to be about that to my eye. (I'm not saying I measured it or anything, but it looks
close enough to one fifth for my taste.)