I am noticing that 90% of my 1200 pages showing up the google serps begin with www.mywebsite I just noticed today that maybe 10-20% for my pages listed in google begin with https://www.mywebsite what gives? Could this lead to a duplicate content issue? I dont know if this help or not but the majority of these https pages...I recently built backlinks to pointing to them. Maybe they are new pages in google index??
The Http vs. Https issue comes from the "sign in" path in your site. Once someone has logged in, it should change to https but never again resets back to http. Since google is showing this, it means that somewhere withing to coding you have programmed (hardcoded) the Https. What I would recommend is to run a "crawler" on you site (gSiteCrawler) and take a look at the resulting list of urls. The pattern of Https will show up and give you a starting point on isolating the problem. If your purchased the ASPX shopping cart, report this as a BUG and get them to fix it. As for Google penalizing you for Dup Content, I don't think so but it will have a major impact on the PR calculation. From a SEO standpoint, this needs to be fixed.