As far as I remember, there was supposed to be a public dump of the MO database just before the migration: http://dumps.mathoverflow.net/ . Not an urgency by any measure, but something that would be quite helpful.
EDIT: Much of the info in the answers is now obsolete. The current go-to place for the public dumps of both mathoverflow and math.stackexchange is https://archive.org/details/stackexchange .