How do I need to change the transparent objects in an inkscape file to be able to export them correctly to pdf? So far it seems the defaults render the transparent objects either invisible or opaque.
Check that it is not rather your PDF reader that is unable to render transparency. Use Adobe Acrobat or Okular (linux), these can render most of the type of transparencies in my experience (including gradients).
The easy silly solution is to export bitmap, then the transparencies over solid objects are rendered. You can then convert to PDF, but this is not scalable anymore.
However, to the best of my knowledge, there is no automatic "robust" way of exporting a scalable PDF with transparencies from inkscape.
You can do it manually though:
A little of a hassle, isn't it? It should be scriptable... See my post at inkscape forum: http://www.inkscapeforum.com/viewtopic.php?f=28&t=15739&e=0
EDIT: OK, thinking a little more of the problem, there's a better way:
This way, you have a combined Bitmap+Scalable Vector document: only the tranparent fill is not scalable, but it will be rendered correctly in PDF viewers.
Since exporting transparent shapes into PDFs still doesn't work properly (at least for me, right now) and the exporting of Bitmaps is (as far as I can tell) a lot of work when you're updating your figure a lot, here's my simple workaround for shapes.
Again, this only works for shapes, not embedded images.
Basically, it boils down to setting the alpha channel of the color instead of it's opacity. I would have thought these are the same property, but apparently they are not.