Couldn't reproduce your problem – which is a pity, because that means I can't suggest anything that might help :-{ Here's what I did:

1. make short .docx with footnotes and transfer file by e-mail
2. open .docx with LibreOffice 4.2.5.2 – footnotes present, but poorly formatted with extra empty paragraphs
3. delete empty paragraphs, save .docx as .docx and as .odt, send both files back by e-mail
4a. open .docx in Word 2010: footnotes present and correct
4b. open .odt in Word 2010, ignore warnings about "corruption": footnotes present and correct

fwiw, the new .docx file includes a separate footnotes.xml; the .odt keeps the footnote information in the main content.xml file. Any back-up files left on the second PC?