Every that I've tried to edit a template or an entry today, Movable Type has dumped a core file and crashed Firefox. This behavior is totally new. A few times in the past week, I've noticed core dumps, which I had never previously seen before. And there is nothing in my error log and activity log (just to be sure) to tell me why Movable Type is behaving like it is. I installed a plugin a few days ago, and I haven't used it, but I disabled it just in case. I also checked mt-check.cgi, and everything seems to be fine. The error persists.

What I want to know is how to find out what Movable Type is struggling to render and how I can fix it.

First off all remove the plugin completely, don't just disable it and see if that solves the problem.

Problems with ImageMagick and PerlMagick can cause core dumps.

I recently (and only recently) began receiving the same erratic behavior. The mt folder on my server was being filled with dozens of these core.### files; some of them up to 165 megs each. This was causing major problems because these files caused a quota overage and therefor the system was unable to write any additional files resulting in the site essentially 'going down.'

Because this behavior simply started out of the blue, I wrote to my hosting provider (with whom I have a good relationship of several years) and they did some tinkering with apache settings, erased the gigs of core files and claimed the issue was resolved. It was not, however, resolved and when commetning stopped working and rebuilds began failing, i manually deleted the core files to get things down to size again.

This was happening on MT 3.3, btw. So to be sure I installed the latest version (non-beta) and upgraded the client's site last night. Everything seemed to work fine for a bit, but sure enough the core.s began falling again this afternoon and I deleted them to attempt a few other solutions.
I wrote to my host again and they responded by saying that the core.xxx files/dumps were actually from SMARTY and advised that i search google for such information/confirmation. They then said if that didn't help then i should contact the support staff for SMARTY.

At this point I have of course searched the Google but regret to report I have not seen anything that helps point me in the right direction toward a solution. Any help or info on this would be EXTREMELY HELPFUL.

A bit late but are you using static or dynamic publishing? Smarty is only used for dynamic.