I just figured out how to install the 4.0.1 update in Mavericks. The problem is that the old Software Update mechanism is completely gone in Mavericks.
1. Install Final Cut Express 4.0 on a computer running Mountain Lion (but I’m sure that Lion or Snow Leopard would work, as well).
2. On the command line use “sudo softwareupdate --download FCE401-4.0.1”.
3. Go to /Library/Updates/ and look in the various folders therein for FinalCutExpress4.0.1Update.pkg. This is about 128 MB in size.
4. Copy that installer .pkg file to your Mavericks computer and double-click.
Presto! This will update your previously installed Final Cut Express 4.0 to Version 4.0.1.