We had the same issue on one of our sites. Here is how I understand it after looking into it and talking to some other SEOs.
The duplicate content Title and Meta description seem to lag any 301 redirects or canonicals that you might implement. We went through a massive site update and had 301s in place for over a year with still "duplicates" showing up in GWT for old and new URLs. Just to be clear, we had the old URLs 301ing to the new ones for over a year.
What we found too, was that if you look into GWT under the top landing pages, we would have old URLs listed there too.
The solution was to put self canonicalizing links on all pages that were not canonicaled to another one. This cleaned thing up over the next month or so. I had checked my 301 redirects. I removed all links to old content on my site, etc.
What is still find are a few more "duplicates" in GWT. This happens on two types of URLs
-
We have to change a URL for some reason - we put in the 301. It takes a while for Google to pick that up and apply it to the duplicate content report. This is even when we see it update in the index pretty quick. As, I said, the duplicate report seems to lag other reports.
-
We still have some very old URLs that it has taken Google a while to "circle back" and check them, see the 301 and the self canonical and fix.
I am honestly flabbergasted at how Google is so slow about this and surprised. I have talked with a bunch of people just to make sure we are not doing anything wrong with our 301s etc. So, while I understand what is happening, and see it improving, I still dont have a good "why" this happens when technically, I have everything straight (as far as I know). The self canonical was the solution, but it seems that a 301 should be enough. I know there are still old links to old content out there, that is the one thing I cannot update, but not sure why.
It is almost like Google has an old sitemap it keeps crawling, but again, I have that cleared out in Google as well 
If you double check all your stuff and if you find anything new, I would love to know!
Cheers!