Won't someone think of the children

Some of the current themes are inappropriate!

Yes. In Series 9, especially. There were way to many stories relating to old ones or about overly convoluted themes. Fair enough if it's once in a while. If we didn't do it, there'd be no Heaven Sent or Midnight, which are both classics. But, when you have something like Zygon Inversion, with a twenty minute labour monologue at the end, it will end up putting some adults off and bore children. The show does pander to fans with stuff like a Genesis sequel and their political opinions, which is kind of it just indoctrinating political views, which a channel funded by a democratic government shouldn't do really.

Yes in a sense of less references to past stories that aren't needed.

I think Doctor Who has always been child appropriate. The continuity in the past couple of seasons hasn't really been a major thing. You could watch The Magician's Apprentice/The Witch's Familiar without ever having seen a Master or Davros story, and you can watch Heaven Sent/Hell Bent without having seen The Day of the Doctor or The End of Time. There are nice references for those of us who are fans, but each story is relatively self contained.

I loved Attack of the Cybermen when I was a kid and it was only the second or third Doctor Who story I'd ever seen at that point. I've seen people criticise it for the gore (which was fantastic for younger me) or the cavalcade of continuity references (which weren't an issue because they were explained within the story). Hell, I was fifteen or so when I first listened to stories like Creatures of Beauty or No Man's Land from Big Finish, they were the kind of stories which I'd pined for on television.

As long as they're good stories, I don't think it's really an issue. It's only bad storytelling that really gets people.

When I had a gig as a reviewer, I was often sent books that were part of a series or a serial story. Part of the challenge of reviewing them - and writing them - was the assumption that part of the readership was going to be completely new to the story. So I started to look out for clues for new readers. It would often take the form of a "What Has Gone Before" section before the Prologue (because there was ALWAYS a Prologue), or some brief remembrances by a character of something that had gone before ("Jane remembered the last time she had heard Bob's voice, before he had disappeared in the forest looking for Spot. Damn, but she missed that dog."), a footnote referencing an earlier volume*, or a conversation between two or more characters as they discuss/ explain what happened (usually one of them will have no idea what is going on because they are new to this volume or were Questing(tm) in another city/ castle/ forest during the Relevant Moment, cf "The Council Of Elrond"). The only time it would really annoy me was if it occurred in a story that gave no indication (in title, branding, or authorial note) that this was part of a series - the Harry Dresden and Sookie Stackhouse novels are particularly egregious here because, despite the fact that the stories in the series are largely self-contained, there are often events in them that affect later novels and the publishers resolutely Refuse. To. Number. The. Books.

Anyway, back to my point...

In this day and age, everyone knows someone who is a hardcore fan of something or is a hardcore fan of something. Series' have mythologies and canons and established continuities and a reasonably aware consumer who doesn't exist in a vacuum only needs to know that this is part of a larger story. That said, you also have to cater for that mythical beast known as "the casual viewer" who will watch something if they happen to be near a tv during broadcast time, and most shows try to make each episode an entry point for those people. Which is why there's a recap when it's necessary, flashbacks to scenes from earlier episodes and "As you know, Bob" conversations that let people or remind them know that clues have been handed out and should no be paid attention to.

I think the danger with any long-established story is that it becomes top-heavy with continuity and also that the production team are continually wanting to push the envelope of what they can do in a story. This is the case in soap operas, which became spectacle-laden to the point of parody some time ago ("I just had the weirdest dream, Pam") so people accept that ridiculous plotlines, sometimes in the guise of "very special episodes" are often part and parcel of the type of story you watch.

To use Doctor Who as a case in point, when it came back in 2005, there was very little to indicate that it was a show with a past history so it rewarded casual viewers with a gradually unfolding story that highlighted a lot of why the Doctor behaved the way he was, but didn't get in the way of the plot too much. As the show went on and you realised that the Doctor was suffering from some sort of post-traumatic stress (regardless of how accurately it was portrayed), I think was when the show went into exploring some serious themes. I don't think the show in its modern incarnation has ever really shied away from going into dark places thematically before, but it usually handles them with some sort of sensitivity: The Empty Child/ Doctor Dances and The Idiot's Lantern touched on things like single motherhood and abuse in ways that were hardly groundbreaking but treated the ideas and the audience with respect and were part of the story rather than the whole story. The classic series also dealt with these ideas but often had to over-egg the metaphor (Nightmare Of Eden, I'm looking at you and your symbolic title) so the audience really had to swallow some medicine without any sugar. Likewise the Zygon Invasion/ Inversion worked so hard at not making parallels that you couldn't help but make them - I loved it, btw, but I could also see that the story tried really hard to come down on the side of passive resistance or civil disobedience as opposed to violent revolution (I'm wondering if The Sunmakers could get commissioned in this day and age) that it did feel a little preachy by the end.

But, at least these days, there aren't being questions asked in Parliament about the suitability of the show for young children.


*The novelisation of The Web Of Fear was the first time I encountered footnotes, FYI.

Seems to be two threads going on at once, here.
One being taboo subjects/themes that DW should or shouldn't be using, and the other being the amount of continuity that appears to be clogging up the episode.

On that we are in complete agreement.
That said, you wouldn't want to park a nine year old in front of a TV version of, say, 'The Pit' or 'The Adventuress of Henrietta Street'. And yes, some corners of the fandom would like that direction to be taken because 'dark and adult'.