I use apt-get update and apt-get upgrade almost every day on my systems at school on broadband.

Use apt-get -s upgrade to simulate your upgrade and see what it is going to install and remove, if it wants to remove a hundred or so packages don't do it! The problem lies not so much with apt-get as much as with knoppix being made from packages from the testing (sarge), and unstable (sid) versions of debian. The only apt-get upgrade problems I have ran into recently are with things like KDE which is hundreds of packages some of which contain the same files so dpkg will error out with an error something like file blah-blah-blah-3.2.1_i386.deb is also in package someting-else. In this instance you have to use dpkg --force-overwrite -i to install the package. Do a search here for force-overwrite to see more info on that command and when people have had to use it.

Also often times with knoppix you have to specify the repository if apt-get install some-package fails try apt-get -t unstable install some-package to get the package from unstable instead of from testing. You can also try apt-get -t unstable -s upgrade and see what that would do.

HTH

~rock