Why do technic bushings have a flat side and a wavy side?
The answer is studs. Note that there are more pieces with the same ability. 



Orientation of the bushing does matter when you run a rotating axle through a technic plate. Have the round side of the bushing pointing towards the studs. Otherwise the axle might lock up. 



Here's an example from set 852 where this technique is used to attach the helicopter's rotor and propeller to an axle.