Sensors
Having a sensor operator could increase your gun/missile/bomb hit chance. Then you can think about trading off between reload speed and accuracy early on.
Alternately, multipurpose Sensors into Electronic Warfare. Electronic Warfare would be used to passively interfere with enemy targeting systems, essentially raising your Evasion by a small amount.
With upgrades, you could also unlock the ability to hack into enemy subsystems, temporarily disabling them like an EMP hit. Hack the enemy door controls and you could open all of their doors to space or a breached room. Shut off their oxygen supplies. Disable the flight controls. Shut off the power to the engines or weapons. Lots of possibilities, but you can only do one at a time, and it's slow!
Having a good Sensors/Electronic Warfare officer would make it much harder for your ship to be hacked into as well.
Of course, EWar shouldn't completely disable door controls if they're hacked into by the AI -- because the AI venting your ship on you would be the cheesiest thing ever. Just set all weapons to autofire at their Ewar room, mash 'close all doors', and pray your own ewar officer can lock them out of the ship or you can destroy their uplink...

Drones
A drone operator would increase the effectiveness of drones - movement speed, attack power, etc. - whether spaceborne or shipboard. Simple.
Cloaking
A skilled cloak operator could squeeze more lifetime out of a cloak and reduce recharge time, maybe boosting the evasion it grants a little (although it's fairly easy to get 100+ evasion chance anyway).
Ed: Changed the thread subject line to be a little clearer.