Another thing SCI can be doing that would greatly help the captain, HELM and WEAP officers is keeping track of what kind of enemies are nearby. When fighting a group of enemies, everyone needs to know which one is the battleship, cruiser, Krelian, Torgoth, etc. This helps the Captain to make good calls on target selection, and helps HELM to know which ship has aft weapons, which ships are more sluggish, etc.
Also, keeping an eye out for nearby (or in some cases, ANY) anomalies is always a good idea. If energy gets low, you don't want to be wasting time trying to find an anomaly.