How do I check programmatically if any document properties of a MS Word 2007 document has changed?

You can certainly check for these kinds of things in some of the events, such as DocumentBeforeClose or WindowSelectionChange, but this may be overkill. Instead, you could just use fields - they will update automatically. For example, go to Insert and then click on Quick Parts and then Field... Go to the Document Information section in the dropdown on the left and choose Title. Then, insert that and go back to the Home tab on the Ribbon and set its style to Title.

You also mention you also want page headers - are those properties you're setting in the Document Panel?