An irate dinosaur wades in the Thames, coming eye-to-eye with Big Ben. A veiled lizard lady-detective and her cockney wife. A Sontaran butler, more used to battle than butlering. And a whizzing blue police box. Of course, it's Doctor Who (Saturday, BBC1). And, just in time for the independence referendum, he's Scottish.

Hello, Peter Capaldi! Welcome back to Saturday nights, welcome to the Tardis and welcome to shouting your lines. Here is the 12th Doctor, finally, the one a generation of children will think of when they cast their minds to the character (mine is Tom Baker). Is he any good? His first word in this opening episode was "Shush", and for the most part, I was happy to do so. He's not bad. He's not bad at all.

As it's the opener, the Doctor is still something of a mess, psychically speaking. He's just been spat out by a dinosaur, and he's still recovering from regeneration. He is confused by, variously, who his companion Clara (Jenna Coleman) is, what a bedroom is ("Who invented this room?! It doesn't make any sense; it's only got a bed in it!"), English accents ("You've all developed a fault!") and so on. Being a Time Lord, however, he has no qualms about the fact that he has arrived in the 1800s, stuck inside a dinosaur.

The dinosaur is not too important, though, which becomes apparent when it spontaneously combusts a few minutes later. The Doctor, taken home and forcibly sedated by Madame Vastra (the lizard lady), jolts awake and escapes through a window. From a bridge over the river, he watches the beast burn, noting the retreat of one figure, a man with half a face, who earlier in the episode had been all too happy to relieve Alfie – one of those chatty London types – of his eyes. After tossing out what may become one of his staple lines this series – "That is not the question" – the Doctor jumps into the Thames in pursuit. The game, Mrs Hudson, is on! (Wait, that's another Steven Moffatt show.)

Long story short, there was once an ancient race of something or other (the Doctor calls them "rubbish robots from the dawn of time") and now a lone relic of that race prowls London, harvesting bits and bobs from the human residents. A bit like a charity mugger then, only instead of a clipboard, this chap has tweezers, and a blowtorch for an arm. The crap robot is trying to get home, to "the promised land, to paradise". It doesn't exist, the Doctor tells him flatly, it's just a silly idea he's absorbed from all those human parts.

Is it fun? Of course it is. Lots of wild to-ing and fro-ing between Capaldi and Coleman, who have solid chemistry, though Capaldi has already ruled out the possibility of romance. "There'll be no flirting," he told the Sunday Times in July. The script supported this, forcefully. The Doctor asks himself: "Why did I choose this face? It's like I'm trying to tell myself something, like I'm trying to make a point." Back home, Vastra talks to Clara, who is still discombobulated by the Doctor's new appearance. "He looked young," she says of No 11. "Who do you think that was for?"

The clearest No Flirting sign comes in the Tardis itself, post-big adventure.

The Doctor: "I've made many mistakes. And it's about time I did something about that. Clara, I'm not your boyfriend."

Clara: "I never thought you were."

The Doctor: "I never said it was your mistake."

There are hints of the darkness in the heart(s) of the Doctor, such as when he abandons Clara in the robot's lair, and when he calls Earth the "planet of the pudding brains". But he has time for jokes. "It's times like this I miss Amy," he mutters at one point, earning a sharp "Who?" from Clara. And he even takes a swipe at my beloved Tom Baker on his quest for an outfit: "I need clothes ... and a big long scarf ... No, I've moved on from that – it looks stupid."

Lest we forget, though, the scheduling suggests a good chunk of the audience is made up of children. And I kept wondering: are kids enjoying this? I remember being terrified when I watched it as a child, but was there this much … other stuff? A fiery lecture on the politics of youth and beauty, delivered by a lizard? There was plenty here to thrill and scare and amuse, like Clara getting whacked in the face by a rolled-up newspaper, but I kept getting yanked out of the moment.

And while we're here, we might as well bring up Moffat's much-reported "woman problem". I cringed when the Doctor called out to the dinosaur: "Oi oi, big, sexy woman!" and mentioned that getting stuck in the Tardis, in the dinosaur's throat, is "mostly how I meet girls". I also hated it when he rescued Clara and mocked the robot for falling for her wiles: "Five foot one and crying – you never stood a chance!" Ugh, why?

This was a promising start, though. A proper rom com-lite farewell for Matt Smith, jokes about Capaldi's eyebrows ("They're crosser than the rest of my face!"), effective hints of the manipulative, knowledgeable Big Bad to come, embodied by Michelle Gomez – all welcome. Not bad at all.