Things that I like to read in a Trek story:
1) Interesting characters that aren't limited to one function. What I mean to say is, even the most dedicated captain in the fleet doesn't sit on the bridge all day, giving orders. The same goes for the other characters.
2) I prefer to read about original characters. There's nothing wrong with the canon ones, but there are already plenty of novels out there dealing with their adventures. So try to make something new.
3) While the characters can be good in what they're doing, try to make it somewhat realistic. I'm well aware that canon Trek isn't always realistic, but 25 year old starship captains, or even worse admirals, is stretching it to say the very least.
4) A sort of philosophical - ethical question in the plot. But don't just add one when it has absolutely nothing to do with the plot. Oh, due try to stay away from religion; there are already too many stories about it, and most of them say "religion is bad". After having read a few dozen of those, it became somewhat boring.
5) Technology. It's an important part of the Trek-verse. Just don't go into technical specifics for no apparent reason. Especially not if it's "existing" technology. If it's something new, tell us something about it, but make sure it doesn't distract us from the actual story.
6) Technology serves the plot, not the other way around.
7) Try to stick to the Trek-rules about stardates, NCC numbers, and warp speeds. I don't want you to start making calculations about warp speed, but make speed-time-distance somewhat plausible.
8) Don't be afraid to explore new places. It's a big place so ships don't always have to visit the same places over and over again.
9) Stay away from the Borg as much as possible; they've suffered enough at the hands of Voyager to be considered a real threat.
10) Don't go too much into the future and past. This being, 10-15 years before TOS begins (I don't like Enterprise), and about the first half of the 25th century (it can be interesting to see how current situations have evolved in lets say 50 years).
11) No Dominion War, there are already enough stories about it; Especially when you consider it's only a 3 year period in almost 100 years of Trek-history (TOS-VOY).
12) While there is nothing wrong with things becoming "darker" on occasion, the Trek-verse has become notably darker with lots and lots of angst in between these last few years without a reason (We can't keep blaming the Borg and Dominion for everything).
13) If the story is in the "future", say 30 years after Nemesis, make sure it's the future. i.e. new ships, technology, political changes, ... In other words, don't du what ST Online does; giving us the 25th century with no new ship to play with. (Even worse, we get the old Constitution refit back.)
14) Don't be afraid to go into the controversial topics.
15) Try to keep spelling and grammar mistakes as low as possible. I might be more forging than others (English is my third language, so I can't expect it to be error-free if I can't do it myself), but it doesn't mean there can be 50 mistakes a paragraph.
If something isn't clear, don't be afraid to ask, I don't bite.