Tower Controller described an unsafe event when traffic cleared to land on a parallel runway; lined up with an occupied runway; initiated a go around and the reporter then failing to hear wrong clearance responses.

Narrative

I was working the Local Control position when the ASDE-X alert sounded. It was advising me that a MD88 on short final was about to land on Runway 22R where I had an aircraft holding in position (LUAW). I questioned the MD88 to verify that he was lined up to land on Runway 22L; his response was 'we're going around'. At that point; the MD88 was at the approach end of Runway 22R and his ARTS tag dropped off and was in the coast list on the RACD. I had the E170; a departure that was airborne off the departure of Runway 22R. The standard SID is; 'upon departure; fly heading 190'. I issued alternate climb out instructions to the E170 'fly runway heading'; it was silent; I did not hear a reply. I told the MD88 to fly 'heading 190' to ensure separation. The MD88 asked me to repeat my instructions and again I told him to fly 'heading 190'. Then as I see the separation was deteriorating; I went back to the E170 and this time issued 'fly heading 270'. During my break; I listened to the unofficial recording and I heard that the MD88 took the instructions for the E170 and the MD88 had read back 'fly runway heading' which I did not hear from my headset at the time of the incident and from the official FAA recordings that was played back to me after the incident. Recommendation; fix the RACD so when an aircraft is on a missed approach; it does not disappear into the coast list. Change the standard SID so that the departure does not climb into the arrival runway. Improvements to the communications equipment so I can hear in my headset incorrect read backs that are being broadcasted and can be heard from other equipment.