That should be the path to the jre directory. And yes, it can be placed in a separate script just as well.
If you place it in /etc/profile, you need to log out first or to do
source /etc/profile
for the changes to take effect.

By the way, did you use update-alternatives to select your new jre over the gcj one? That can make a difference too.

Run
java -version
and
(as root)
echo $JRE_HOME
If neither points to your jre6, then there is some more work to be done.

OK, I backed out JRE6 and re-installed JRE5, as bathory suggested, and that solved my "no visible output" problem, although I still can't run applets requiring JRE6. Does your $JRE_HOME fix also address the "no visible output" problem in a different way, or are we looking at two different problems here?

No, the entry in /etc/profile is most useful for running java applications (azureus , hjsplit , etc.). Have you checked update-alternatives? There's a galternatives front-end in the repositories that may make things a bit more intuitive.

Well, since reverting to 1.5 fixed my browser display problem, I'll settle for that for the time being. I looked at the update-alternatives info and will keep it in mind; before actually using it, though, I need to get to where I understand it better. I'll keep the $JRE_HOME thing in mind as well, but so far the only problem I'm having is with the browser; either I'm not using any java programs outside of the browser or they're working OK.

BTW, I also tried using the GNU Java plugin (libgcjwebplugin.so). It worked fine in some cases, but one of the ones I especially wanted to get going (a word puzzle program on one of the newspaper websites) it did a clear-and-refresh about two or three times a second; VERY annoying. I'll be exploring that alternative as well, but I won't be holding my breath.