Currently the accepted thought is about 1000 ly., but new findings are challenging that figure on two fronts. The measuring of pulsars located above and below the galaxy indicate a thickness at least twice than what was previously believed, something on the order of 6000 ly or more.
Here is one source, but there are others: http://www.cosmosmagazine.com/news/m...er-we-thought/
Also, it's being discussed that the Milky Way might not be the thin disk with a bulge in the middle as previously thought, but more uniform in thickness throughout (in light of that my 3000 ly. approximation might not be off much).
Our understanding of the Milky Way is constantly evolving. Indeed what we know of the Milky Way is barely a hundred years old. Over the years ever new information has changed our ideas of its shape and size and composition. We once thought the galaxy was pinwheel spiral, but now it appears it might be more of a barred spiral. It was once believed to be only about 10,000 ly. across, but that estimate has long since been revised to about 100,000 ly. It was earlier believed we were a bit closer to the edge but now we're thought to be a bit more centred between the rim and the centre.
Also it would be interesting to know what Sam Peeples (who wrote WNMHGB) and the TOS writers thought in terms of the galaxy's shape and size. Certainly at best they only had a 1960's understanding of the Milky Way and not our current understanding from more than forty years of research since.