The plots, and the Doctor himself, are so incoherent that even I barely know what the hell just happened at the end of an episode, and I'm normally the guy in the room who is explaining the plot twists to others.
I haven't had any problems understanding what happens in each episode. In fact, I find the two new series by Steven Moffat to be considerably better than the old Russel T. Davies series.
Russel T. Davies was infamous for "Doctor Ex Machina" plots, in which the Doctor would pull technobabble solutions out of his ass at the last minute. His villains were either re-introduced monsters from old Doctor Who episodes, or extremely uninteresting evil aliens who were entirely interchangeable.
Steven Moffat actually attempts to write science fiction, in that the Doctor's solutions are based on rules set up earlier in the episode, rather than rectum-derived technobabble. The viewer gets all the information the Doctor gets, so when he reveals the solution there's a genuine feeling of "Oh, now that's quite clever". Moffat's monsters also typically have some kind of interesting gimmick and often have some relation to the real world, giving them a certain scare factor that's not present in Davies' generic aliens.