Where do Minecraft texture packs go on OS X?
I poked around and discovered a new folder:
~/Library/Application Support/minecraft/texturepacks/
Putting the texture packs you download in this folder makes them appear in the menu. Don't extract the files, just leave the .zip there.
Previous to this update, you would put Minecraft.app into a folder called "Minecraft" along with all the files for the texture pack, and launch Minecraft.app from there. However, I don't know if this is still the case with this version.
(The button also doesn't do anything for me.)