Bug 779680 removed usage of nsIDOMWindowUtils.goOnline() in about:neterror. This had been used to go online when clicking "try again" after a page failed to load due to be in Offline Mode. However, browser_bug435325.js, which tests that functionality, still makes reference to nsIDOMWindowUtils in its log output. Arguably, that test should be in moved to /browser/ (from docshell), since that functionality was moved into browser chrome.
Is there some sort of B2G API that can be used to kick Firefox online so you don't have to rely on something in /browser ?
You mean WebAPI? None that I'm aware of, nor any plans. At least in terms of Firefox, Offline Mode is kinda-sorta being slowly deprecated anyway (as evidenced by its move to the Developer Tools menu).
Created attachment 653657 [details] [diff] [review] Patch v1