tl;dr A bug in the Adobe Reader plugin causes IE9 to not load PDF files in the browser, which can be fixed by disabling chunked transfer encoding in Sitecore config.
About 5 months ago we upgraded a Sitecore 6.4 solution to 7.0. I can’t remember why we didn’t go with 7.1 since it had been released, but I think it may have been because some of the modules we were using (mainly WFFM and ECM) were not ready at the time. Regardless, the issue we faced would have been the same.
The site we were working on was very media heavy – lots of images and PDFs (in fact this was an ideal candidate for CDN, but that’s another story…). During testing we were getting reports of the links to PDF’s no longer working, but intermittently and only for some people. Eventually we narrowed it down to IE9 browsers only.