The RCS thrusters on the Apollo Service Module were positioned approximately around the center of mass of the ship, such that translational maneuvers wouldn't unnecessarily rotate the ship. While the position of the center of mass would vary as propellant and other consumables were used, a small amount of differential thrust from the RCS thrusters could maintain the ship's attitude against the resulting torque.
Those mass shifts were small, however, compared to the movement of the center of mass with the Apollo LM attached.
When the Apollo CSM and LM were docked en route to the moon, did the control systems automatically utilize the LM's RCS thrusters in combination with the CSM's to maintain attitude during translation maneuvers, or was the LM entirely dead weight?
After LM extraction, translational RCS maneuvers may not have been needed; any small midcourse corrections that were performed on the RCS could be done by rotating the ship into the correct orientation, then using pure forward thrust (i.e. thrusting through the shifted center of mass).
The Apollo 13 crew commented on the difficulty of maneuvering the joined ship using only the LM's thrusters; presumably the CSM RCS was entirely shut down at that point, but if the CSM were undamaged and powered-up, could the ship be flown with coordinated RCS using the LM's controls?