Tie Fighter extended on X-Wing in that it had not only primary and secondary objectives, but also bonus objectives, given out by an advisor of the Emperor.
Unlike the other ones, the bonus objectives are mostly hidden in their explicit form ("Identify freighter X") until completed. You pretty much had to derive them from the briefing and the debriefing (these usually contained some spoilers, assuming you failed the mission). The only hard value you could see was the number of these objectives ("you completed 1/6 bonus objectives").
I find it often quite hard to figure them all out and complete them all. Yet I do try to complete at least some of them and I do rise in the Emperor's ranks.
Does that mean the game only keeps track of you completing at least one on each mission? (Or how many necessary for the advisor to give you a positive debriefing.) Do you rise in the ranks faster if you complete more? Is it worth going through the extra effort to do them all?
Note: of course I am aware that you do not get any real in-game benefits from working for the Emperor at all. The game is from a time when gamers could still be motiviated without these cheap tricks. ;) The cutscenes are the reward, I guess.