Recent versions of Slackware are still maintained. So security issues will be resolved in patched packages, whichyou can find on the Slackware ftp and mirrors. The packages are in the Slackware-<version>/patches/packages directory. Download those and use upgradepkg <name of packages you want to upgrade> to update your packages. After that, there shouldn't be a known security issue on your system left.
Subscribing to the Slackware-security mailinglist is very usefull as well. It will send an email when there are new upgraded packages with location of these packages, description of the problem and how to install these packages.
There's an online archive at http://www.slackware.com/security/li...ecurity&y=2003