1) You shouldn't really run current until you are familiar with Slackware. Slackware does things slightly differently, Use 12.2 preferably.
2) Slackware builds KDE 4 'as is', without all the patches the other distros apply to make it actually usable.
3) You probably don't have hardware acceleration enabled on your graphics card. What is the output of
glxinfo | grep direct
4) KDE Network Manager is useless and has been useless for years. Use wicd, if you want something graphical, and only wicd, as it can conflict with the Slackware networks management scripts. It actually works quite well.