I've read somewhere that PDF 1.3 flattens? Maybe this can explain the grey boxes? Using this option is not really preferable since I would like to use hyperlinks in the document and PDF 1.3 doesn't support that. This solves the grey box problem, but the quality problem remains.

Exporting in press quality both problems occur.

Exporting in the standard High Quality settings both problems occur.

This happens to images, not to text (vector I suppose?)

Image quality is very good in Preview, but bad in Adobe Acrobat X (grained edges).

Some images with a transparent background get a grey box around them (not all, seems random).

All objects with an outer glow get a grey box around them (these include external images but also squares created in InDesign).

Next to that, the image quality is very good in Apple Preview, but it's pretty bad in Adobe Acrobat X and Adobe Reader 11.

The problem is that grey boxes appear around some objects. I've exported tens (if not hundreds) of PDFs with InDesign and I've never experienced this problem.

Export indesign to powerpoint