The QGIS Intersection tool is not working for two shapefiles in Version 2.2 or 2.4 (haven't tried earlier versions). I get a new shapefile with all the attributes, but no features. However, when I use ArcMap with the two shapefiles, the intersection happens correctly. The shapefiles are both in the same coordinate system. I have used the QGIS tool with success with other shapefiles that I got from a QGIS tutorial.
The shapefiles that I'm using are all from the Data BC website. I've uploaded two samples to http://vulnerablevancouver.ca/qgis_intersection/ if anyone wants to have a look. I put the zip files there that include the metadata.