I prefer the upgrade method using one tool for download the packages installed in my system and upgrade automatically. I described some steps to get Slackware-current working.
I used the slackpkg tool ( slackpkg.sourceforge.net )
If you have mozilla( removed in Slackware Current ) installed in your system please remove before start this procedure and after upgrade all packapge use slackpkg to install the Firefox-1.0.6( included in Slackware Current).
1 - Download slackpkg
2 - Install this package
3 - Edit /etc/slackpkg/mirrors and add the below line.
This mirror is very fast for me...
4 - We must update the slackpkg database
5 - Upgrade the Slackware-10.1 to Current
slackpkg upgrade slackware
6 - Installing mozilla-firefox
slackpkg install mozilla-firefox