I like this idea Darkthunder though I think I would seperate the science/medical area's myself.
For science the officer in question could use their abilities in studying anchient ruins on new worlds, or for that matter ruins of a more comtemporary theme to deduce what happened to it's inhabitants. Also Science officers can find new resources in the form of metals or liquids that have properties for further study etc. On ship their skills with sensors could help locate vulnerable points in hostile alien caft to assist the tactical officer and perform experiments in the ships labratories when not under combat pressures on the bridge.
Medical will have some similarites to the above, healing injured personnel on the ground or dealing with massive numbers of injuries as people are brought into sickbay from areas of the ship during ship to ship combat. This would entail treating npc's as well as players in this situation. When not in combat, the good doctor can research cures for diseases, study new alien anatomy and so on.
there would be many other things other officers such as the tactical/security officer, captain and others could do on and off ship, but I wont go into this here unless your interested in further elaboration.
All in all though I like what you have written here.
Zach -- I agree what you have said here too.