The Weekend's TV: The Killing II, Sat, BBC4 Frontline Medicine, Sun, BBC2

I have a hunch about the particular kind of fervour that The Killing generated among its fans on its first outing.

It was good, of course, and sometimes very good indeed. It had a compelling central character in Sarah Lund and a story explored in real emotional detail. It also gave its early adopters the thrill of discovery, of stumbling on a treasure that not everyone knew about. But there was something else besides, which really cemented its grip on its viewers. It had subtitles and that meant that – unless you were fluent in Danish – you couldn't half-watch it. We've got increasingly used to doing this recently, dividing our attention between a television screen and a laptop and a smartphone, and it's happened so gradually that I think we've almost forgotten how rewarding it can be to really pay attention to something. (I wonder too whether this phenomenon might have something to with the high reputation of The Wire in this country, which, thanks to the Baltimore accents, either had to be watched with the DVD subtitles turned on, or with the concentration of a codebreaker).

Now The Killing is back, with awards on the shelf and Lund on the front cover of the Radio Times, and the big question, apart from "where's her old sweater gone?", is whether it can repay the scrutiny a second time. Like the first series, this one started with one of the stock tropes of the television thriller – a panicked 999 call from a distressed man who can't find his wife. "There's blood everywhere," he says breathily and then, "What have I done?" But The Killing has shown before that it can rise above the clichés it deploys, so there's no cause for real anxiety yet, even if it seems like a long time before Lund herself appears, exiled to some backwater where she's doing traffic checks at a ferry terminal. Cliché Two arrives – the reluctant detective, who says she's turned her back on all that but is then sucked in by the curiosities of the case. From the moment that one of her colleagues says, "If he's covered in blood we're halfway there", you know that Lund is in for the duration, and that we're not even a 10th of the way to the truth.

The writers haven't strayed very far from the formula that worked last time. It isn't long before the murder, apparently an open-and-shut domestic, turns out to have unexplained connections to a parallel political storyline – the attempts of a newly appointed justice minister to negotiate a tricky anti-terrorism bill into law. His coalition partners can't agree whether civil liberties should take a back seat to public safety (and public prejudice) and when an Islamist group posts a video of the murdered woman, reading out a statement about vengeance for "the suffering Denmark has caused in Palestine, Iraq and Afghanistan", the possibilities for compromise diminish still further. Another man, an ex-soldier, is found murdered and there's an unexplained link to another veteran, currently being held in prison after a psychotic episode. Lund is very glum and still seems to prefer torchlight to all other forms of illumination. But after two hours of paying close attention, I'm still not inclined to seek distraction elsewhere.

There seems to be a hint that wartime trauma lies at the heart of the mystery, a subject explored more clinically in Frontline Medicine, in which Michael Mosley visits Afghanistan to find out how battlefield surgery is teaching British doctors new ways to keep people alive. Apparently, soldiers are less likely to die from a wound now than they've ever been, even though IED wounds are horrendous. Mosley reported with clarity on new techniques but also reacted emotionally to what he saw, visibly shaken after an "Op Minimise" loudspeaker announcement, which tells the camp that communications with the UK are temporarily suspended, so that the relatives of those who can't be saved hear from the Army first.