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.
All of the data (minus deleted stuff) should also be accessible via our API.
I'm not sure off the top of my head what the options are (if any) for setting up a site-specific data dump. Please let me know if the data explorer is not sufficient for your needs once MathOverflow can be queried there.
Note that these dumps are a torrent for the entire stack exchange network; there's a separate file inside for each site. Most bittorrent clients can be told to only download specific files, and this should let you just pull out the MathOverflow specific parts.