Seems I spoke too soon...
I decided to investigate this a bit further, and it seems I am having the same issue. I have published a locator service based off some local street data (the data and locator service are both Web Mercator). I tested the located in ArcMap first - works fine. When I call the locator service from the old "Locator" widget, it finds candidates, and shows the correct location. When I call the exact same service form the new search box (in the Header Widget XML), it finds the candidates, but drives the map to near 0,0 lat/lon (off the coast of Africa in the Atlantic Ocean).
So, it seems like the code behind the search box in the Header Widget is messing up the conversion from lat/lon to Web Mercator (or the other way round) - it's interpreting a lon/lat as a Web Mercator Easting/Northing.
This makes the new search box (which is a great idea) unusable as-is.
Chris