This blog post is a bit late, but yes, the latest Overviewer does support the latest Minecraft version 1.6.
As some may know, Minecraft 1.6 adds Resource Packs, and thus the format for texture packs and has changed. Since Overviewer pulls textures straight from the Minecraft client assets, this necessitated a change in Overviewer. And as we're not fans of keeping lots of code around for backwards comparability, this means the latest versions of Overviewer will not support reading textures from Minecraft clients or texture packs from 1.5 and before.
This typically isn't a big deal—as people update their clients and update Overviewer, things will just work. If you do not want to upgrade your Minecraft client or texture packs, then you should not upgrade to the latest Overviewer.
As always, the best place to get help, ask questions, or get involved is on IRC!
(For posterity, the most recent build that supports 1.5 is a147ca4a. Downloads: Win64. Also, to be clear, the newer Overviewer will still render older worlds, you just need the new textures.)