Ive never really had issues with not getting credit except for one time I sank a ship in shallow water and it struck bottom before it 'sunk'.
Then again I generally only play campaign mode.
Some of the mission objectives are kind of obscure there is a sticky post in the FAQ about "how to complete a mission" might be worth browsing.
As far as a better captains log ? Hell yes, for one thing Id like to be able to enter my own notes, I also dislike how the entrys are sorted. Page after page of contact reports interspersed with my own reports is messy. Yes I am aware they can be sorted by sent / recieved. Still pages of contact reports hundred of miles from my station are of no importance to my log yet they are full of this 'spam'.
Forgot to add ; Welcome to the forums !
(Paragraphs are a good thing

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