How to repair anchor holes and re-mount bathroom tissue dispenser
If you  are repairing the wall and re-installing the tissue dispenser it would be wise to "multi-task" the repair.

Cut the damaged area to an opening smaller than the length of the dispensers screw holes. Cut a piece of 1/2 or 3/4 inch plywood 2 inches longer and slightly narrower than the cut you just made. Secure the plywood into the wall incision so that it will be held in place by a screw at each end of the wall opening (the plywood should extend an equal distance behind the drywall).

The newly installed plywood can now be used to attach a drywall plug and then the dispenser.