I would be curious to know whether, now that links to MO appear in the footer of every SE 2.0 site, and in the "hot questions" list of the Stack Exchange button, the rate of inappropriate questions has increased. By inappropriate, I mean things like calculus homework, "what's wrong with this proof that 0=1", etc.
This would presumably need to be measured by an SE team member, although the MO moderators can also offer their qualitative opinion (as far as I remember from my time as a math.SE mod, there are no migration / closing statistics available to site moderators). While any current information about this would be welcome, the switch to SE 2.0 is still quite recent, so perhaps the data should be reviewed in a few weeks to get a better sense of the effect of the switch.
The questions to be counted would be those that were migrated to math.SE (though of course this has only been an option since the switch), and those that were simply closed due to inappropriateness. Now, the range of close options used on inappropriate questions was, and is, wide, and I think several of those close options from MathOverflow 1.0 do not exist anymore as a result of the switch, which increases the difficulty of automating the tabulation of inappropriate questions that were closed. One thing that may help would be to do a site-wide search for comments such as "Crossposted to math.SE [link]" because this would correlate well to questions that were ultimately closed for being inappropriate.
I suspect the answer will be that this rate has increased. I seem to remember that part of the agreement behind the switch was that MathOverflow would be invisible to the rest of the SE 2.0 network (though not the other way around), precisely to avoid this effect. Was this condition of the agreement discarded? Do people feel that it would be good to implement (regardless of its previous status)?
I am using the term "switch", instead of "migration", to avoid confusion with the migration of questions between different sites.