Database Issues

[ZiNgA BuRgA]

I'm not sure I can really help with partially importing tables.  You're probably bound to get issues whether you realise them immediately or not (unfortunately, MyBB does not enforce integrity constraints at the DB level).
Threadfields should mostly import fine I'd say.  If it's templates, well just redo them I guess.  Maybe you could pull in templates in the Global Templateset only.