FAR local controller described operational error event when clearing a departure for takeoff with traffic on final; reporter noting the need to improve airport scanning before take off clearances are issued.

Narrative

I had a Learjet in the local pattern with numerous inbounds and departures. Aircraft X who was following my Learjet was cleared to land. After my Learjet did a touch and go on Runway 36; I decided there was a gap before the landing Aircraft X to depart a small aircraft that was full length on Runway 36 westbound; because there was not a wake turbulence delay. After I cleared him for takeoff; a call from an aircraft from a nearby airport came over the frequency which I told to contact approach on a different frequency. After that transmission; I knew that I wanted to get Aircraft Y who was at Intersection B3 and Runway 36 out before the Learjet came around again. I observed the Cessna that I had cleared for takeoff just off the departure end and then proceeded to clear Aircraft Y for takeoff at the intersection. After the takeoff clearance I keyed up to my RADAR controller to point out the Learjet who was going to be slightly outside my airspace with his wide pattern during which the Aircraft X said that he was going around due to Aircraft Y approaching the runway at the B3 Intersection. Aircraft Y was past the hold short line but did not appear to be on the runway when Aircraft X passed by him. I told Aircraft X to enter right traffic for Runway 36 and he came around again and landed. Recommendation; I believe the call from the aircraft from a different airport; the point out with RADAR briefly distracted me along with not scanning effectively before clearing Aircraft Y for takeoff contributed to this event. My recommendation would be to advise my Ground Controller no intersection departures when there are jets in the pattern and wake turbulence delays are possible. This adds a complexity of extending the jet traffic which you might not have room to do when busy; to allow the wake turbulence delay to expire. Also; [the development of] a better scan technique when clearing aircraft for takeoff.