Re: Who is the target audience?
You're spot on, here - Doctor Who is a kids' show, always has been, always will be. It's going wrong because it's trying, and failing, to appeal to adults, rendering it incomprehensible to children (quoth my youngest: "THIS IS BORING!").
I think it might also be suffering becuase the stories are crushed into 35/40 minutes, and thus have a hurried resolution - I don't necessarily want a return to the 4 cliffhangers + 1 resolution, of my childhood, but the decent stories of the past 2 episodes have had very rushed conclusions ("it's a flag, he's a soldier, I'll salute him and he'll fall apart" / "I'll leap out of my tardis, brandish my magic wand*, and they'll fall apart"), so maybe it ought to be split over 2 nights (Fri/Sat or Sat/Sun)? It's in the wrong timeslot, anyway - it should come before Strictly!
*about time the Sonic Screwdriver went, too - occassionally well used, mostly just a crutch for lazy writing