The nessus package is an excellent package for checking known security problems. Install on one machine both nessus (the client) and nessusd (the server).
For nessusd you need to create a user account using nessusd-adduser. One suggestion is to simply create a user with the same name as your user account (e.g., kayon). Then start the daemon (server) with:
# nessusd -D
Note that this daemon is not automatically run within the /etc/init.d framework.
As a user start up the nessus client and login with your user name. Go to the Target selection tab and type in a list of hosts you wish to check, comma separated. If you want to test all machine on your network, try something like 188.8.131.52/24.
After you click Start the scan the checking is initiated. Eventually a report will be presented. You can save the report in various formats, including LATEX.
The testing is extensive and the report provides suggestions for eliminating security holes.