There's no way (that I see) to access full details about a mission once it's accepted. Example: the Beginner Combat Practice mission says Kannik and another type of collector bot count, but 2 other kinds of bots yield a bonus. Once I've taken the mission the bot types aren't mentioned.

if you type something (almost anything) to your mission computer, it should re-list your objectives for you as well as give you an abort option.

it also relists for you when you reach the ammount needed for the next xp bonus.

[edit] during beginner/advanced combat missions.

That doesn't work for all missions, though. The recon/spy missions in particular don't work well with that...