There are many specific qualities in the most recent Star Trek series that I would change.  Here they are, in no particular order:

• No More Birthday Parties on the Bridge

What kind of naval vessel has birthday parties for civilians immediately after an unresolved attack by an alien entity?  Would Picard ever let that happen?  Kirk?  It's saccharine nonsense, and has no part in Star Trek.  That's not to say that parties can't happen, or that characters can't celebrate.  But when the annoying, transparently irritating alien vagabond storms unannounced onto the bridge with a birthday cake in his arms, protocol demands that he get a public dressing-down by the Captain.  If my Captain had been in command of Voyager, Neelix and Kes would have been kicked out of the ship the very moment they became a liability.

• Death to Cute

Cuteness makes me sick. 

• Science!

There is nothing more disappointing and rhetorically weak than for the crew to save the day by inverting the feedback polarity of the warp field or some other such made-up, fake technical nonsense.  Someone in Star Trek Central decided that fans like that crap, and so now every single Star Trek episode has bucketloads of it.  

In truth, there is a very small minority of fans who like the technobabble; they're mocked openly by movies like Galaxy Quest, because it's an ultimately silly thing to be so daggurmed fascinated by.  

It's made up!  Sure, some of it is grounded in science, but it's 9/10 completely invented by people whose sole job is to invent new things for characters to say while they punch buttons on a keypad. 

It's not necessary.  Problems need to be solved by people, not science.  On TOS, Kirk argued with a crazy robot and made it fry itself.  On Voyager, a minor character uses Science! to change the polarity of the crazy robot's power couplings.  Which is the stronger, more memorable solution to the same problem?  The answer is obvious.  My Star Trek would keep Science! to the absolute minimum.     

• Please Excuse Me While I Tell You How I Feel...

In the same episode of Voyager outlined above, the Commander and Neelix stop their Very Important Mission to talk about Neelix's jealousy.  Other than it being a completely unrelated and unnecessary plot point between two minor characters, it made the pacing of the episode grind to a halt while they discussed their feelings.  Bad writing.

Here are a couple of scenes that I would like to see:    

Minor Character: Captain, I have a problem.

Captain: What's the problem?

MC: I think I suddenly feel an unjustified and nonsensical attraction to a woman onboard the ship who-

Captain (looking as though something suddenly smells very badly): Uh, go talk to someone who cares, crewman.  I have a ship to run.

or

Minor Character: Captain, I'm feeling like this job is too much for me to handle.  I can't bypass the tachyon conduits without thinking about my long-lost twin brother.

Captain: What's your name again?

MC: John Doe.   

Captain: OK, John Doe.  Pack your things and say goodbye to your friends.  You're off the ship at the next starbase.  

Of course, I'm being facetious.  But I think a Captain doesn't have time or patience to deal with every little crew problem that comes up.  Isn't that why they have a chain of command?  Why is the hierarchy almost ignored in Star Trek?  Using it in my Trek would definitely add a new dimension of drama.