If you want to do this upgrade, I'd upgrade to Slackware-13.37 first, using the hints in UPGRADE.txt, and then upgrade 13.37 to -current once that is complete. During each release cycle, several packages are added and removed, so to move from 13.37 to current in the second step, you should read the Changelog closely to see what steps you might need to take to run current.
There will likely be Slackbuilds which do not work in the latest -current, especially since there has been an upgrade to a new GCC which breaks certain build scripts. Additionally, the usual warning that SlackBuilds.org does not support -current still applied. That being said, many people run current and use SlackBuilds without much problem. For programs that you have compiled yourself, the same caveats apply.
If you follow UPGRADE.txt and Changelog notes you should have a -current system running fairly easily. It's hard to say if you will have problems with your other applications without knowing what they are, but I shouldn't think it will be a major issue.