CMH local controller described a potential opposite direction conflict when a C172 departing from an intersection departed on the wrong runway; unnoticed because of several distracting factors.

Narrative

I received flight strip from Clearance Delivery on a C172 (CMH.....; requesting 7;000). I immediately noticed that it was marked incorrectly with an 'E'; indicating East Gate above 10;000; thus the pilot would have been issued North Departure frequency of 125.95. I walked over to Clearance Delivery and advised that this aircraft should have been issued South Departure frequency of 119.15; and that the strip should have been marked 'ZZV' or 'ZV'. Then I heard Clearance Delivery speaking with the pilot again; and again issuing the incorrect frequency of 125.95. I figured I would correct this error myself; and discuss with Clearance Delivery when he had a free moment. When the aircraft called for taxi from General Aviation ramp on south side of Runway 28L; I had inbound General Aviation traffic that would probably exit Runway 28L at either C3 or B3. So instead of giving short taxi for a B3 Intersection departure; I gave the C172 taxi instructions for a B2 Intersection departure. The pilot responds with a simple 'Roger; call sign.' I recall that pilot hesitated; approaching Taxiway B. I had an aircraft repositioning to a hangar; so I then revised my clearance to the C172 to hold short of the B2 Intersection so that other aircraft could enter his ramp. All was working well. In fact; the Clearance Delivery had gotten relieved and observed my head on situation on Taxiway B and informed me of it. I told him I appreciated his team work in bring this to my attention. When the C172 advised ready for takeoff; I had a helicopter that was southeast of the field; westbound. So I opted to use the incorrect North RADAR frequency that Clearance Delivery had issued; and turn the C172 northbound so he would not be a factor with the helicopter. The C172 questioned my clearance about turning right to 360; so I restated the clearance. I figured that was cleared up; so I began to discuss the incorrect frequency assignment with the Developmental Controller who had been working Clearance Delivery. However; he didn't seem to understand. I then scanned for the C172; figuring he should be abeam of our (mid-field) Tower; and after not seeing him right away; I looked down the runway and saw him airborne; eastbound; the pilot had departed Runway 10R. I had an air carrier inbound for 28L about six miles out; so I immediately turned the C172 to a 050 heading and coordinated. Had the regional jet been in closer; this would have been an extremely bad situation. The somewhat hazy day; combined with our very dusty shades being down; the sun out of the west; a little aircraft blending into the runway pavement; the departure frequency error distraction; my trying to teach the Developmental Controller in between transmissions; feeling assured that the pilot had been clearly told twice to depart Runway 28L; resulted in me not critically watching which way the pilot turned on the runway to depart. I think if I had not been attempting to teach the Developmental Controller; I would have been more focused on watching the pilot; and may have caught the wrong way turn on the runway. However; pilot education would go a long way in this situation.