Transmission goes in to forward fine, sometime have trouble getting it into neutral. When I try to put it in reverse all I here is a clicking noise. I think it is the centrifical clutch, but would like to make sure.

 

Nope, wouldnt be that. The centrifical clutch doesnt know forwards and backwards...it always spins the same direction, its mounted on the end of the crankshaft.
Id say the shifter linkage needs adjustment.

 

I have the belt housing cover off, and when I do get it in reverse the clutch plate and belt all spin in the opposite direction then when it is in forward.

 

You got me. Thats a new one on me. The motor, which drives the primary pulley, is attached to the end of the crankshaft. The motor will always rotate in the same direction. Going into reverse wont make the motor reverse its direction. The secondary pulley is attached to the geared transmission, where the direction of rotation can be reversed.
But as far as i know, the belt and pulleys always go the same direction...a 4 stroke motor cant be run in the reverse direction.
Usually this is just a simple adjustment of the shift linkage, to allow enough movement to firmly select reverse.

Did you try having it in reverse...motor off, and push it to see which way it spins? and then put it in high...motor off..and push it to see it spin the other way?

If you run the motor, and look at the pulley direction of spin..itll always go the same direction, whether its high, low, nuetral or reverse. But using the wheels to spin the tranny, itll go either direction...this is what allows engine braking. But if the motor is delivering power, the pulleys go one way only.