A few ideas:
I would give data more capabilities, like a built in tricorder and communicator. He would also interface directly with the ship's computer. His emotions, rather than being granted by an emotion chip, would be restricted by one he is unable to remove.
Wesley would not be a child genius and would suffer the most horrendous acne. He is a burden on Beverly.
Bev did not want to be on the Enterprise and her resentment toward Picard would occasionally froth to the surface, causing moments of aukward silence.
Troi would harbour some serious emotional issues, because of her talent, but would never be able to let it show because of her position. She remains onboard to be close to Riker, with whom she is obsessed. Riker has pitty for her, and looks out for her, but they both know they'll never be together, and he looks, searches for a way out.
Picard is deeply troubled too. Extremely repressed he retreats to long dead worlds at every opportunity, wishing he too had gone the way of their inhabitants.
I would also change the ambient sounds on the ship, the low hum of the engine sounds would be replaced with an electrical buzz that would increase in volume when ever a character is seen alone.
I would use more natural light on the ship, giving the impression of illumination from local stars, similar to Generations, the light source would move, altering the shadows and creating an illusion of ship motion.
There would be more shots of the crew stood by windows, looking out wistfully on the rest of the universe. The starscapes would be more vibrant too, with vast clusters of stars and nebula etc. The trek galaxy would be populated by all the fantastic sights the Hubble Telescope has shown us.
CGI would augment the alien characters to give them unhuman features. Impossibly shaped torsos, longer/shorter necks/legs/arms etc. Bigger eyes, extra fingers. Extra limbs. Anything that can't be done with bits of rubber.
The turbo lifts would have two sets of doors and a small gap between the carriage and the deck, like real elevators. The ship schematic in engineering would be 3D and zoomable.