I'd say I look for something a bit different
in a fanfic, but not too different
if you know what I mean.
The problem with Star Trek fanfic is that so many stories tend to revolve around the same thing - a new crew is assembled to take charge of a new ship and off they go, which is fine but the market can get a little saturated and everything blends into everything else.
So it's nice to see something that takes the existing Star Trek scenario and has a little fun with it with some 'outside the box' thinking.
But then I don't personally enjoy things that go too far, killing off main characters and the like. I personally like my fanfic to be something that could be
shown in an episode if you know what I mean.
And of course the use ridiculous ten mile long behemoth Starfleet ships with eighty phaser cannons and a stockpile of 500,000 torpedoes more or less goes without saying as a big no no.