Doug: Revit is pretty smart, but it's not that smart. You can mirror a whole building ok, so that the *model* is properly mirrored.
To do this simply draw a ref. plane in a site plan view to be the center of your mirror axis, then go to a 3D axon view, select the whole building, go back to the site plan view and then click Mirror on the toolbar and the pick the ref. plane... bam! mirrored building!
However this probably will screw up your sections, elevations, and callouts, for they all remain in their old locations and pointing their old directions. Mirroring a whole project is not something that's easy in Revit once you've gotten most of the ways into CD's. Heck it's not something that's easy in any CAD software. It's a lot of work to mirror an entire project properly.
Another way to crack this egg would be to export all your detailed callouts as DWG files, then mirror the model, edit your elevations & sections to be proper, them import all your detailed callout views into blank drafting views and then re-reference there locations within the building. That way at least you've benefiting from the Revit model being mirrored, but not having to re-do all those detailed callouts.
good luck!
