Piersall was identified in the script as a lieutenant commander, but was mistakenly given the pips for an officer with the rank of lieutenant junior grade. He seemed to have been in command of the Prometheus for the mission - it is unlikely that either a lieutenant jg or a lieutenant commander would be the captain of a ship as large as a Nebula-class. The script says that he is merely "in charge" of the bridge. He may well have been the first officer or second officer.
According to a line cut from the episode, Piersall was impressed with the work that Miles O'Brien had done on the Prometheus's warp engines.