I'm not an expert or anything, but in my brief experience with K-Meleon I've learned it doesn't seem to support many javascript conventions like many scripts that are intended to launch a pop-up window. This could be part of what's happening in your case. You may also come accross a page that's moved & has a message explaining the new URL & that says something to the effect of "Click here if you're not automatically forwarded in xx seconds", this is usually a meta-refresh tag which also doesn't seem to work in K-Meleon.
What's more, either my copy is configured unusually, or K-Meleon doesn't have Java intergrated by default. That would mean applets are out of the question, but that's not a huge problem for me since I find applets to be a bit hostile for my liking anyway.
FYI: Javascript & Java are different things, so fixing one of these issues won't cover it all.
I've usually got some means of working around just about any Javascript roadblocks, but I'm hoping the impending new version won't inherit these flaws. In the meantime you might try pulling-up the Resources section (
http://kmeleon.sourceforge.net/resources/ ) & download those Java runtime environments, that might help with some of your applet problems.