When upgrading Thunderbird, FireFox, or SeaMonkey, at times you'll receive an error similar to:
Update Failed: One or more files could not be updated. Please make sure that all other applications are closed and that you have permission to modify files, and then restart Firefox to try again


(see step 4 if you're just having this error and an upgrade had previously been done)
The program must close to allow a previous installation attempt to complete. Please restart.

There have been several fixes posted online and not all of them work; however I've gotten around the error by doing the following:
1. Delete the data in the "updates" directory:
In Windows:
Thunderbird: C:\Program Files\Mozilla Thunderbird\updates\0
FireFox: C:\Program Files\Mozilla Firefox\updates\0

2. Download the latest copy of the product from an official source, such as http://www.mozilla.com/en-US/products/
3. Install the product from scratch, by default it should utilize your current profile.
4. After the install, delete the xpicleanup.dat and xpicleanup.exe files from the product directories.
5. Start the product and you should be golden.

You can find several other startups and their errors here