From MozillaZine Knowledge Base
The Software Update feature allows you to automatically update your Mozilla application and installed add-ons (extensions and themes, but not plugins). Software Update is available in Firefox, Thunderbird, and SeaMonkey 2. This article describes how to configure and run Software Update and discusses problems that can occur during or after an update.
Checking for updates
By default, Software Update periodically checks for updates and notifies you when an update is found. You can modify these settings in your Options/Preferences via the "Advanced -> Update" preference panel (Firefox and Thunderbird) or the "Software Installation" panel (SeaMonkey 2). If you want to force an update check, choose "Help -> Check for Updates...".
The update process
When an update is found, follow the on-screen instructions to download and install the update. The application will need to restart to apply the update, but you can choose to restart later by pressing the Later button.
Software Update not working properly
Software Update problems can sometimes be resolved by simply restarting the computer and then reopening your Mozilla application.  Other update problems can be fixed by downloading the latest version of Firefox, Thunderbird, or SeaMonkey and installing the new version "on top of" your current version  .
If the problem continues, you can manually reset the Software Update feature by closing your Mozilla application and deleting the "updates" folder and the two files "active-update.xml" and "updates.xml", which can be found in one of these locations (using Firefox as an example):
This will solve a number of Software Update problems, including:
Software Update Failed
Update Failed. Something is trying to trick Firefox into accepting an insecure update
A Software Update "Update Failed" error, Something is trying to trick Firefox into accepting an insecure update. Please contract your network provider and seek help, has been reported to Mozilla in bug 653830 (under investigation at time of writing). See also the forum discussions here and here.
Software Update Failed. One or more files could not be updated
If you see a Software Update Failed error with the message, One or more files could not be updated. (or, in Firefox 3, The update could not be installed), try ending all instances of Firefox or Thunderbird (or reboot the computer) and then restart your Mozilla application, to see if that allows the update to complete. Also try closing any other running programs that may be interfering with the update process, such as the applications listed below.
Software that can cause updates to fail
Other installed applications can disrupt the update process and cause the Software Update Failed error. See this forum topic for other causes and solutions.
Other running programs that may interfere with the update process include:
Software Update Failed. The update could not be installed
Some users may see a "Software Update Failed" dialog after restarting Firefox with the message, The update could not be installed. Please make sure there are no other copies of Firefox running on your computer, and then restart Firefox to try again. If you see this dialog, end any Firefox processes (or reboot the computer) and restart Firefox.
If the issue is still not resolved and you are using Windows Vista, try the following: 
Another possible solution is to reset the Software Update feature by ending all Firefox processes and then removing "active-update.xml", "updates.xml" and the "updates" folder from the appropriate folder locations (see above). As a last resort, download the latest version of Firefox from www.mozilla.com and install it over your current version.
AUS Update XML File Malformed 200
The message, AUS: Update XML File Malformed (200) can sometimes appear during a check for updates. This is a "catch-all" update error which can occur for different reasons such as being in "offline" mode, network problems, or not being signed on with your Master password (if you've set one up) before the update check . Software Update requires a secure connection so, if you are also receiving errors on webmail login pages, bank sites or other secure (https) sites (e.g. https://addons.mozilla.org) see Error loading secure sites.
If Software Update errors persist, you can download the latest version of Firefox or Thunderbird from www.mozilla.com and install it "on top of" your current version, instead of using the Software Update feature.
Related bug reports include:
Problems after an update
The following issues can occur after a Firefox or Thunderbird update (see the linked articles for details).
Configuring Software Update
Update channels - Advanced
Updates can be retrieved from a number of different update channels. To check which channel you are on, look in about:config at app.update.channel. This determines what kind of updates you will receive. The current update channels are:
Please be aware that the nightly, and to a lesser extent aurora and beta, channels may install builds that have serious bugs. The application may be non-functional and/or result in your profile being corrupted. See Profile_backup for information to safeguard your data, and see the daily builds threads at the Mozillazine forums for the current status of the builds: Firefox, Thunderbird.
The installer/zip/tar/dmg that you last used to install Firefox, Thunderbird, or SeaMonkey determines what update channel you start on. It does this by installing the file "channel-prefs.js" into <installation directory>\defaults\pref. With the new rapid-release system, you will stay on that channel, thus receive a "bump" to the next version when the repositories are migrated. On the aurora and beta channels, this also implies that a lot of patches are landing at that time (including API and string changes) to synchronize the repositories with the new versions they are carrying.
Note that you cannot change channel using about:config. Instead, you can use the Update Channel Changer extension (go to Help -> Check for Updates -> Change Update Channel). Alternatively, you can edit the channel-prefs.js file with a text editor.
If you tried to change the channel by editing channel-prefs.js and there is no app.update.channel pref in about:config, or it has not changed, then the channel-prefs.js file needs fixing. Either install the Update Channel Changer, or open <installation directory>\defaults\pref\channel-prefs.js in a text editor like Notepad, making sure that it has two lines like this (for the nightly channel):
//@line 2 "/cygdrive/c/builds/tinderbox/Fx-Mozilla1.8/WINNT_5.2_Depend/mozilla/browser/app/profile/channel-prefs.js" pref("app.update.channel", "nightly");
Only the // on the first line is important because it is a comment. If the value in about:config has still not changed, then right click and reset the preference - this removes the profile value that is masking the application one.
Update URLs - Advanced
Early in the testing cycle of the new software update, testers were required to enter a special update url into the preference app.update.url. This is no longer the case and in fact now that preference is almost ignored. Only the setting from the file firefox.js (or all-thunderbird.js) in the installation directory is used. This is so the application always uses the same updates regardless of what user profile you are running with.