When cutting mortises for mortise and tenon joints, it's easy to make sure that the mortise is centered in your piece. Simply cut the mortise from one side. Then, when done, flip the piece and cut the mortise from the other side. If your positioning was perfect, this second cut will do nothing (which is fine). But if your positioning was slightly off (as mine always seems to be), this will result in a centered joint.

Another thing to remember when cutting mortise and tenon joints, always cut your mortises first. Cut the tenons afterwards and adjust them (using scrap test pieces) to fit the resulting mortises.