I am seeing this problem as well with the built-in viewer. It appears Opera 36 uses the new version of Chrome's PDF viewer, and it does not as seem as quick or stable as the old one.
Sometimes the PDF's just take a very long time to load (far longer than previously for identical files), and other times it only loads if I refresh the PDF URI after trying to load it from a link. Occasionally, it doesn't load at all, and there remains just a white screen.
If I load a PDF file that is on my local machine, it works, but takes a few seconds longer than on the old PDF viewer.
Switching between the plugin options "load all content" and "click to play" makes no difference, except that with click-to-play, the white screen still occurs and then once the PDF reader does load, I need to click to display it. I suppose this proves the issue is at a level below that.
I had the Per-plugin content settings extension installed so that I could have click-to-play for all plugins except PDF (which would always just load). Disabling and even uninstalling the extension has had no effect. I will note that the extension's options page is now also a blank screen on Opera 36, whereas on Opera 35 and earlier it displayed fine. I hope the extension has not made some permanent changes to my installation that removing the extension did not undo...
I'm on Opera 36 stable, Windows 10 Pro 64-bit. Machine/connection is not slow (Core i7, 8GB RAM, premium SSD, 100mbit fibre).