Exploration – the pushing out of new boundaries of the frontier
Carrying supplies and cargo to outposts and distant colonies
Carrying passengers
Diplomatic and trade missions
Patrol along marked or disputed boundaries
Mediation and negotiation
Responding to planetary emergencies
Responding to ships in distress
Routine visits to planets/colonies/space stations
Scientific missions
Defensive action against threats to Federation planets
Military manoeuvres
Testing of new equipment
Training missions
Serving as a police/security force where requested
Serving as good will ambassadors/showing the flag
Crisis control
Terrorist/hostage rescue
Don’ts
Psi-forces or psychic/mystical powers
Galaxy policemen
Fantasy instead of Sci-fi
Swords and Sorcery
Treating deep space as the local neighbourhood
Melodrama
Skipping the Prime Directive
Plots involving whole civilizations
Technology as the villain
Miscellanea
Hidden in chapter two
Languages: If a character chooses to be proficient in linguistics, have them speak a minimum of languages equal to their Reason score.
Fewer subspace relays mean slower communication.
What does the character use the holodeck for?
Time dilatation under warp: Problems and inconveniences.
How does character use the replicator?
Soul food?
Decorations?
Clothing?
From Forum
Also, consult p. 201 on how to get NPC Crew involved. You can combine this with creating advantages (which can be created when you need help, cf. p. 191, so this will be applicable to assist, I think) and use crew as they were your Starship (cf. p. 169: Starships can generate advantages).
Ideas
Languages don’t need to be spoken, have them whistled, for example.