I was looking for a new browser and Opera was looking very promising... until I stumbled across this glitch. Really? Not being able to open PDF files in my computer's default PDF viewer program is unacceptable!
Temporary workaround (or maybe definitive because this issue was not taken into account): double click the pdf files on download drop-down list.
When you have "Open PDF files in the default PDF viewer application" checked and in your computer setting setup the default PDF app you want to use - Mine will open Adobe Acrobat Pro
Which Opera version have you installed?