-Don't wank off the doctor every episode. It's all right to have an episode every now and then where you can get away with portraying the doctor as the weird alien time traveling entity that is truly dangerous, but not every episode has to be "A good man goes to war." The character is called the doctor for a reason. Focusing on how good they are at being an omnicidal warlord is... More in the spirit of the master than the doctor. There should not be a grand celebration or comedic reference to how many people the doctor has killed too often otherwise it undermines the whole shame of the "you would make a good dalek" episodes they like to remake every now and then.
-On a related degree don't treat the doctor's intelligence as some kind of superpower where he does 5d chess throughout time. He's not a marvel superhero, 9th and 10th doctor made it very clear he's smart but not that smart, and however smart he is, he or she is still bound by the wibbly wobbly laws of physics.
And my one potentially controversial take
-Refocus away from the grand narratives back to episodic fun where each episode could be its own self-contained story. It would make the show much more fun for casual viewers who wouldn't need to understand vast pieces of lore just to get what is going on
So some further thoughts. I'm now at the Capaldi era and have found myself skipping large chunks of episodes. Particularly the Zygon invasion episode pair - the sole redeeming feature of which was the Dr's speech towards the end. This is likely a personal gripe, but the whole 'they're just a splinter group, the rest are 100% happy with us' rhetoric came across as too real-world propagandist for me. Instead of subtle allegory, we had John Cena.
Note that I'm not commenting on the validity of the rhetoric. Mainly because I think it's too thorny, sensitive, and complicated to make a simple declarative statement and then lol into the sunset like the Dr did.
Anywho. LW, see above, notes that we ought to see grand narratives interspersed with 'episodic fun,' with a good balance struck. They did this quite well with Matt Smith era Who - the episodes had some reference to the overarching narrative, but it was usually just a snapshot of a mysterious crack at the end. And when they did epic narrative, the narrative was epic.
An example of episodic Smith would be the Van Gogh episode. They meet the artist, they relate to him, lie in a field and see the swirling colours of the cosmos ----- and fail to change the course of Vincent's life. Personally, I found it very emotive - and I know it to be a fan favourite.
Capaldi doesn't do this. We get Danny Pink, which was well done - the Good Soldier meets the Fleeing Quasi-Deserter - and we get Missy, who is emotive in a whole different way. But post-Pink, none of the episodic episodes carry any emotive weight. They are whodunnits, curiosities, but not.... gripping.
So yep, this is my assessment thus far. Not sure if I'll be able to break into the post-Capaldi seasons. But we'll see - I've only just managed to stomach the Zygons.
Edit: I've now seen to the end of the Capaldi era. It gets a lot better. The tone with Clara and Capaldi-Doctor was horribly off, and while Bill Potts has always struck me as a paper-thin character, Nardole brings enough depth for both of them. Which is surprising because I was prepared to dislike the character.