I've just struck a very similar problem --- could save the document in 2003 (.doc) format, but trying to save in .docx resulted in an endless loop of SaveAs dialogs popping up, and no document actually being saved.
The document had pictures but no formulas, and and first I didn't have a clue which parts of the document were corrupted.
If it helps others, I was able to fix the problem by doing the following:
- With an open document, choose Save As.
- Set to save in .docx format.
- [Very important!] Tick the box titled “Maintain Compatibility with Previous Versions of Word”. Word then allowed me to save the document, but indicated it'd fixed some errors. At this point, I could click the Details button for a list of errors which had been fixed.
This enabled me to save a document in Word 2010 format. The document was saved in Compatibility mode, but I could easily revert that by choosing File/Info/Convert to convert it to a full 2010-format document.