It sound as if you are not embedding the font properly. Of course this should be automatic when exporting unless the font is restricted. What font are you using?
Do the missing characters (the ones that turn into empty boxes) show up anywhere else in the same font?
And you really are exporting, right, not printing, to PDF?
I too am expericing this.
just to explain a little in how I got this my process is
I start with a PDF that I need to grab data from, I open in Illustraitor and copy the content I need in to InDesign. it all seems to work even in preview, but when i export into PDF sometimes some of the characters turn into the boxes