Or something else altogether.
I'm hoping to find a pattern in a series of elusive errors on my SQL 2005 server.
SQL Server stack dumps occur when internal consitency problems are detected, not on errors (ie. not when @@ERROR changes to non-zero). There are ways to force it to dump on error if you must, you have to contact product support and ask how, but I very highly doubt is necessary.
Why not you ask what is the elusive error you are seeing and perhaps the community can help you with that instead.