I've been thinking and here are my ideas for improving the new Doctor Who:
1. Spend time on individual stories. The old show had half-hour episodes and most of the good stories had more than 4 episodes to them. The new show follows the standard TV format of a different story for every episode (the over-arching plots notwithstanding), with occasional 2-parters. Make every story at least a 2-3 parter and take your time on things.
2. Spend time building worlds. Stop making up new menaces every episode. Spend time in a place and make it believable. Show some complexity and nuance. The new shows world's, alien races, etc., seem largely made up of whimsical after-thoughts. They're throwaways. Get better script-writers. Russell T Davies was awful. Steven Moffatt is a little better.
3. Dispense with over-arching plots between stories. Every season seems to have a plot like this which isn't any better than the individual stories. The Key to Time was great but this new show needs to master the basics before attempting something like that.
4. 2 year moratorium on the Daleks. Unfortunately, the Daleks and Davros became stock villains in the old series; they're even worse now. When you bring them back, make them interesting, complex, and genuinely scary. I think the last Dalek story where they were really menacing was Genesis of the Daleks.
5. Stop making the Doctor out to be some kind of god who is at the center of everything. This was an unfortunate carry-over from the latter years of the old show, especially McCoy's time. The Doctor was more interesting, IMO, when nobody knew him and he seemed more detached and inscrutable.
6. Make Doctor Who asexual again. The sexualization of Doctor Who has not made it more titillating, just more conventional. Again, like his god-like status, it makes the Doctor less interesting.
7. Make the next Doctor some ugly old curmudgeon. In the old show, the only Doctor who was a "looker" was Peter Davidson and that was when the show was at its nadir. You can afford to lose the teeny-boppers if you actually make a gripping, intelligent show. No Doctors under 50, please.