Mechanic reports he missed noticing damage to one of the elevator assemblies on a B737-300; during a Detailed Visual Inspection. Damage was caused by the potable water servicing door panel previously departing the aircraft.

Narrative

While working a deferred seat back on Aircraft Y; I was notified by Operations that Aircraft X had arrived minus the potable water door. I was involved with Aircraft Y near departure time of Aircraft X. After finishing the deferral of the seat back on Aircraft Y; I went to the gate where Aircraft X was. I went over to the aircraft and saw the potable water door missing part of one hinge and the bonding wire were the only things that remained. I did a detailed visual inspection of the potable water service area pan and the fuselage skin around the adjacent area. I walked back to where I could see the APU shroud drain. Visually looked at that for signs of damage because it was almost in direct line with the door cutout. I didn't see any damage to it; so I looked up to the tail cone of the APU exhaust from that point. I did not specifically look at the elevators on either side of the fuselage and I don't know why. I removed the hinge and bonding wire; completed the logbook with the appropriate CDL. The damage discovered by a flight crew on walkaround 2 flights later. I was notified of the incident by my manager.