I've never embedded a PDF like this myself and I agree its probably not best practice. In general I view a PDF as an external document or printable version of something. Rather then embedding the PDF, can't you just put the content directly into your page then give an optional PDF download link? Embedding a PDF is not a common thing, in fact this is the first time I've heard of it.
I think the main issue is each browser seems to have its own (or none at all) pdf embedding logic. That is why it works in some and not in others. It could also be dependent on having Adobe Acrobat vs. another PDF program, I really don't know.