I access the same Firefox profile in Ubuntu 12.04 and Windows 8.1 (Windows fast startup disabled). I have the newest version of Firefox (26.0) on each system.
Every time I launch Firefox in Ubuntu after using the profile in Windows, I notice that autoscrolling is disabled. So I have to manually enable it every time after using my profile in Windows.
Conversely, every time I launch Firefox in Windows after using the profile in Ubuntu, I'm asked whether I would like to set Firefox as my default browser. I choose "No", first making sure that there is no check mark next to "Always perform this check when starting Firefox". I have to do this every time after using my profile in Ubuntu, despite the fact that if I check my preferences in either OS, "Always check to see if Firefox is the default browser on startup" is not enabled. Note that Firefox is my default browser in Ubuntu but not in Windows, but I have no need for Firefox to check whether it's the default every time it starts in either OS.
I don't know for sure whether these problems are related, but it seems likely that they are. Is there a way that I can keep these settings constant, so they don't reset every time I switch operating systems?
I asked about this one week ago on the Firefox Support forum but haven't found an answer so far. Since I know a lot of Ubuntu/Windows dual-booters frequent Ask Ubuntu, I thought this question might be useful here for others facing the same problem.