The cause of the problem seems to be that nsIDownloadManager has been deprecated as of Firefox 26.

https://developer.mozilla.org/en-US/docs/XPCOM_Interface_Reference/nsIDownloadManager?redirectlocale=en-US&redirectslug=nsIDownloadManager

If we want to support Firefox 26 and higher as a platform, things that use nsIDownloadManager and
nsIDownload will need to be changed to use Downloads.jsm when those interfaces are not available.
(Will need to support both, for sake of compatibility with older versions as well.)