Whenever we see the "other side" of the mirror, the crew sees no problem while the captain is derisive or intensely annoyed.
My players didnt really care, prefering to get by on their wits and ingenuity (seeing how they knew little of Trek but what they gathered from when i watched tv, Dorm life was boring during the day)
The more advanced government came across as a mildly arrogant deus ex machina, or doing the heavy work while the characters provided a "lower deck" view. Id bet theyd get ticked for being treated as too limited, immature or primitive if the campaign was more tech driven
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"Mission? what mission?"
"Save the galaxy."
"AGAIN?!?!?!?!"