PROBLEM: You want to remove any inactive people from your friends list.
SOLUTION: Go to your friends page. Look for anyone with a mystery man as there photo. Hover your cursor over their name. If they are still active, then a little window will pop-up with some basic information about the person. If nothing pops-up, then they are inactive. At that point, you can click on their name and a window will pop-up telling you they are inactive and asking if you want to unfriend them.
NOTE: This works as of 1/15/2013. Facebook changes stuff all the time, so I can't guarantee it will work for you when you read this.
This means they are still active.
This means they are not active and you can click on the unfriend link.