Comment 23 for bug 1059051

webapp depends on the box with the user's email, it means that is strongly interface dependant. It should rely on the 'class' or 'id' attribute instead of a DOM tree. Everytime google change it's interface, everything stop to work.

My suggested fix is to change the line #146 to this:
gmaillogin = document.evaluate('//div[@class="gb_Q"]', document, null, XPathResult.ANY_UNORDERED_NODE_TYPE, null).singleNodeValue.textContent;

and the line #153 to this:
gappslogin = document.evaluate('//span[@id="gbgs4dn"]', document, null, XPathResult.ANY_UNORDERED_NODE_TYPE, null).singleNodeValue.textContent;

Tested here, it fix for both personal account and google apps. Don't know if this ID and Class will change, but is more reliable than the tree.