When measuring control throws with a control surface deflection meter, is it best to take measurement at the widest part of the control surface or somewhere in the middle of the control surface? Let's say that I want to measure the deflection of the rudder on a P-51 Mustang. Do I take measurement near the bottom of the rudder where it is widest or in the middle?

you should measure it at it's widest chord. But for a rudder, the throws aren't that critical. The elevator & ailerons are much more sensitive to excessive throws. Most people try to get as much throw from the rudder as mechanically possible.