Minor version updates cover major version downloads. It might seem like doing us a favor as the latest version supposedly has the latest fixes. But what happens in the Firefox situation is, AddOns break with the minor update. Wanting working AddOns back one tries to download the previous version only to find it's gone.
One may say "save the old installer." But if you use Update from the Firefox Help menu you don't get an installer. It updates with no way to back it off.
If this is the case Firefox needs an "undo last update" button. It's really frustrating to hunt around for an hour to find a download version that should still be posted. Firefox 27.0 should be directly under Firefox 27.0.1.
Now I've vented I feel better. At least until the next time I have to update.
Any add-ons breaking on an update is incredibly rare in Firefox these days (I can't remember the last time it happened to me). Unless the add-on author chose some poor settings for Max and Min versions. For those, it may be worth looking into whether there is an alternate. Or whether you really need the add-on at all.
You should never use an outdated version of Firefox anymore, other than for testing on known-safe websites. Each version of Firefox is insecure and outdated as soon as the new one is released, along with the public disclosure of the security issues fixed. As soon as that information is public (its not public before the patch is released), the script toolkits used to implement the hacks on websites are updated to include an exploit for the recently-patched security issue.
Sometimes, the impossible can become possible, if you're awesome!