Why is the Mooney's signature tail profile different from most planes?
The best explanation I've heard is that at high angles of attack the rudder is nearly vertical providing the pilot better yaw authority.  I don't know whether this is true or not but it makes for a good story, doesn't it?

The story goes something like this:As the plane pitches up, the rudder, being slanted "forward," moves closer to a vertical position and provides better directional control at low speeds.  Conversely, at high angles of attack a swept tail (and rudder) moves further away from a vertical position and is, in theory, less effective.

Some go on to speculate that the leading edge of the vertical stab, being un-swept, protrudes further into undisturbed airflow at high AOA/low airspeeds which may slightly enhance the pilot's ability to control yaw at the edge of a stall.

I've never spun a Mooney (I did complete my CFI in an M20F/201) nor do I have a burning desire to do so.  I imagine that it's not a friendly spinner.  Catching the spin early would be critical in a slippery air frame like a Mooney.

A brief online search of Mooney tail lore yields everything from pure marketing to discussion of wetted area to better directional control during landing to spin recovery/prevention to "those swept tails provide no speed benefit and are simply designed to look good."

Here is one discussion (of many) on a Mooney forum regarding the tail design: http://mooneyspace.com/topic/9905-mooney-tail-aerodynamics-not-backwards/

I doubt very much that it's simply a marketing gimmick (although, it could be as simple as that!).

I believe that the explanation I've relayed here is merely "somewhat plausible" as it was gleaned from hours of beer-fueled hangar talk and some Google searching...not exactly a scientifically rigorous method of research.  I have no credible references and, as far as I know, no data exists to back any of it up.