After about two years of increasingly recurring kernel panics while using Firefox, I think have solved the problem, thanks to some googling and advice from others.

I spent a while keeping an eye on this thread:
https://bugzilla.mozilla.org/show_bug.cgi?id=1111808

The kernel panics were blamed on sites that used WebGL, combined with imacs that had an ATI Radeon X1600 graphics card.

A couple days ago I found another site which offered what I hope is the solution:

https://superuser.com/questions/73518/ati-x1600-driver-problem-on-mac

Here the advice was to use a program that allows you to adjust the fan speed, the assumption being that excess heat was causing the graphics card (or something) to become too warm, thus setting of a kernel panic. For me, this only happened in Firefox, and I had long ago disabled hardware acceleration in Firefox prefs. I did disable WebGL through Firefox config a long time ago, but I don't remember how to re-enable it. I don't remember how to check if it is enabled.

Regardless, I downloaded Macs Fan Control and used the default settings. So far no kernel panics, not even on sites which were guaranteed to cause them. I'm hoping for the best.

Wow, what a long, terrible problem that may finally be solved. So many people shaking their heads at my old machine. It lives!

Old machine? What do you mean, old machine?

OK, so it didn't work. B&H.com reliably causes a kernel panic on Firefox 39. Doesn't happen with Safari 5 or Opera 25.

I think this one's unfixable. Whatever the programmers at Firefox have done, it's crashing my computer.

Have you filed a "grievance" with Bugzilla?
It may also be that they're aware of the issue but haven't yet been able to correct it.

I posted a message on Bugzilla. I don't know what the process is for filing an official grievance. I don't expect a problem to be solved for someone using an old comptuer and an old version of Firefox.

From what I've read online, and tried myself, it has something to with Firefox, certain web sites, webGL, and the graphics driver in the Radeon X1600. I thought heat might be a factor, but I guess not. Even if I disable webGL and hardware acceleration, I stll get kernel panics.

The solution is for certain sites to use Opera or Safari.

The solution to this is at https://support.mozilla.org/en-US/kb/upgrade-graphics-drivers-use-hardware-acceleration

You have to disable hardware acceleration and webGL.

But you just said

I was wrong. I tried it yesterday. The B&H site reliably crashes my Mac. As soon as I turned off webGL, I could use the site.

1) Turn off hardware acceleration in Firefox prefs, under Advanced.

2) Disable WebGL:

a) In the address bar, type "about:config" and press Return.
b) At "void warranty warning" continue.
c) In the Filter box, type "webgl.disabled"
d) Double click on the "webgl.disabled" item to switch it to true.

3) Restart Firefox