Using 2.7.1
I had the same problem.
More specifically, I can add galleries just fine, as well as create thumbnails. All permissions were fine and the nextgen add function was working just as recent as 2 days prior to this issue. ALL of the galleries that were on the page were working.
The only issue was that when I clicked to see insert gallery, the actual "insert" button/text, was gone. The gallery lists still appeared, but that was gone. I couldn't manually insert it either.
So, I deactivated all the plugins except nextgen and it worked. One by one, I re-activated them and found out that the plugin "WP-CUMULUS" caused it not to work. I don't need cumulus, so I just let it go. There was no update available for cumulus either, as I have the latest version.