By subscribing to the security alert mailing lists, and keeping current, you can do a lot towards securing your machine. If you pay attention to your log files and run something like tripwire regularly, you can do even more.
A reasonable level of computer security is not difficult to maintain on a home machine. More effort is required on business machines, but Linux can indeed be a secure platform. Due to the nature of Linux development, security fixes often come out much faster than they do on commercial operating systems, making Linux an ideal platform when security is a requirement.
It is unfortunate that this document does not discuss some other issues, such as the legal ones. While this certainly affects an administrator, it does not uniquely affect a Linux system administrator. The legal issues are real ones. Luckily, there is an incredible amount of information on this topic available elsewhere already.
Some things you should always be sure to do when taking on a security project:
Keeping up-to-date with the flood of security topics can be an overwhelming task. Take a piece at a time, and prioritize what needs to be done. Choosing the obvious holes to fix first is a good start.
Remember, just because you have all the latest software updates installed, does not mean your machines are secure. There will always be new software exploits, as well as uneducated users who choose poor passwords. Continual inspection and attentiveness is required.