I've been through a few versions of Slackware on my Asus EeePC and I must, despite that fact that every has been having lots of trouble (or so I've heard) configuring Linux on it, it hasn't been all that bad for me. One problem that continues to persist is that the brightness setting is weird. It doesn't like to display on full brightness most the time, and when I try to change the brightness (function keys or OS function), it goes through 3 'mini-cycles'. I've tried the Alien eeepc-acpi-scripts slackbuild a while back and it didn't work for me before. While searching for another solution, I found this thread on the Ubuntu forums:
But the major fix that seems to be working for them involves editing GRUB (which I don't have). Another post suggests simply updating the BIOS, but the BIOS updater is a Windows executable, and I'm not quite sure how he pulled it off in Linux.