One thing I've heard conflicting advice on is how to handle a job search for two people simultaneously; especially the strategy of things like: when do you mention your situation to the departments in question? In your cover letter? When you're invited to an interview? At the interview?
As usual, people should be specific about what kind of institutions and which nations they have in mind with their advice. Also, presumably strategy differs a bit depending on whether the second person is a mathematician, or in a different discipline; it would be great to hear about both of those cases.