As a very rough example of how minigames and skill levels might usefully interact, here are some of the things an Ops officer might be able to say:
Sensors 0 (which everyone has): (detects nothing at long range)
Sensors I: "Captain, long-range sensors show some unusual activity ahead, but I can't identify it yet."
Sensors II: "Captain, I'm picking up something unusual on long-range scans in the theta band ahead of our current position."
Sensors III: "Captain, I'm reading some kind of subspace flux directly ahead, about a light-year from here."
Sensors IV: "Captain, long-range sensors are detecting subspace shield radiation directly ahead, 1.2 light-years away -- it's on a Borg shield frequency."
Based on the specificity of the information, the captain could decide to investigate, to run for cover, to hold position and call for backup, or to ignore the sensor readings and go do something else that looks like more fun. Having a dedicated Ops officer (i.e., a player whose character has chosen to pick up a broad mix of useful support skills) could make the game more fun for everyone aboard that ship. And making minigame results somewhat dependent on a character's skill level creates an incentive to improve one's character.
Definitely still plenty of room for refinement of these ideas, though.