As I open a PDF file in Illustrator CS6, it displays it rotated 90 degrees CW. If I rotate the artboard and content back to normal for editing and save it, Acrobat Reader displays the file rotated 90 degrees CCW. Where does this behaviour come from, and how do I deal with it?
It comes from the originating application. When whatever app wrote the PDF it incorrectly wrote the portrait/landscape setting or rotation. Illustrator is reading whatever rotation is in the PDF and saving it as altered if you change it.
If you want Reader to NOT see the altered rotation. Open the PDF with Illustrator. Rotate it however you'd like. Then Save As an .ai file. Then save as a PDF again. This should eliminate the stray, incorrect data. If you open a PDF, then simply save it, the bad data is retained.
I'm not certain about Reader, but with Acrobat you can choose File > Properties and see what app generated the PDF.
If you're trying to batch process a lot of files you can open the PDFs in Adobe Acrobat Pro and Save As Other "PDF/E". If you look at it's settings this has a tick box to 'Apply Corrections'. It seemed to fix the error in the file so that it opens in landscape in Illustrator. Less steps than manually rotating each one.