The major noticeable difference between a symmetrical airfoil section and an unsymmetrical one is in pitching moment.

An asymmetrical airfoil section has a higher pitching moment per unit lift than a symmetrical airfoil section. This moment will mean a higher torsional force on the rotor root end, which will require more blade mass to counteract. This higher torsional force will also be fed into the pitch change mechanism, requiring a stronger (and thus heavier) control mechanism, and the addition of hydraulic controls, in most cases, to allow full pilot control against these higher forces. Asymmetric sections can provide higher lift per degree of angle of attack, but you'll pay for it in a heavier rotor system. In helicopter engineering, everything is a trade-off. (Nick Lappos told me a few weeks ago that he was going to post something here about that concept...)

On an asymmetrical blade, the chordwise center of pressure will vary according to the pitch. For instance, at 0º the center of pressure might be 45% of chord and at 15º it might be 25% of chord The center of the feathering axis might then be located in the midpoint of the centers of pressure. This will probably cause high loading on the pitch change mechanism in for ward flight since the advancing blade will have a low pitch and a negative moment while the other blade has a high pitch and positive moment. In other words the moments are not canceling each other but are working together.