Malware and Spam
Of all the security problems a server might have, malware and spam are particularly despicable. Few things are worse than finding out you have a virus or other malware infecting your system.
Linux servers do not have to worry about nearly as many viruses as Windows servers do. Nevertheless, you should still take some precautions so that your Windows desktop users do not get viruses passed through your mail server or other transports.
Viruses aside, other types of malware can and will attack your server if you are not prepared. Botnets, trojans, and rootkits are just a few of the nasty creatures that could infect your server and use it to spread itself or attack other servers. Moreover, some malware may even use your server to send spam.
Spam is a nasty problem that any system with a mail server will need to handle. You can install spam detection tools and possibly even use secondary tools like DNS blacklists. Many anti-spam systems require training in order to be effective. Once you have trained your system, you should have few false positive and also little spam delivered to users.