The week in TV: Roadkill; DNA; The Same Sky; Out of Her Mind and more

<span>Photograph: AP</span>
Photograph: AP

Roadkill (BBC One) | iPlayer
DNA (BBC Four) | iPlayer
The Same Sky (More4) | All 4
Out of Her Mind (BBC Two) | iPlayer
Count Basie: Through His Own Eyes (BBC Four) | iPlayer

At least Roadkill isn’t as bad as Collateral, David Hare’s last big-budget BBC outing. It doesn’t water-cannon us with message – asylum seekers good, security services bad – or strain so hard to avoid cliched cops that it creates an unbelievable one. And it’s blessed with Hugh Laurie and Helen McCrory, who almost redeem it from itself.

And it doesn’t, for once, wear its Tory-hating credentials on its ragged academic sleeve; indeed, Hare has said that he tried, for once, to get to grips with the mindset of a “good” or at least maverick Tory. And Laurie plays Peter Laurence MP with a superb credibility: a corrupt Tory MP, yes, with secret plans to carve up the NHS to benefit American privatisation, but a charmer of a man, too, with the common touch and a genuine zeal to make a difference for the better, particularly in prisons, against the stultifying hand of the civil service.

Because of this, the promise of a crusading reformist PM in the making, with a secret (and secretly charming) daughter in one of his own prisons, I could forgive the tick-boxing – the spiky journo, the corrupt prison private-security firm, the haughty plotting between Tory chairman and arms-dealer cartoon villain.

But I can’t forgive the many plot impossibilities. Laurence’s own defence lawyer, having won a famous case, getting an anonymous call saying “look into him” and somehow agreeing. The driver to the justice secretary, presumably having signed something or other, being asked who his mistress was and just blurting it out. Laurence himself saying with wicked glee, early on after a prison riot: “Let’s hope there are injuries. Better still, fatalities”, which, after you’ve watched the whole, sits entirely against his character.

Collateral was, oddly enough, Hare’s first-ever TV serial after a life of rightly garlanded plays and screenplays. And I’m sadly reminded of little so much as the time Dorothy Parker and pal Robert Benchley decamped from New York to California, to write B-movie plots under that golden sun and make some easy money: surely such talents, such wits, could outwrite formulaic by-numbers stuff? After a slew of rejections and flops, they fled back to the rain and Parker ruefully concluded: “Seems shit has its own integrity.”

DNA, in Danish, French and Polish with subtitles, is, I’m convinced, our new The Bridge for double-bill Saturday-night autumn binges. It’s not as if we’ve anywhere else to go, but, quite apart from that, it’s every bit as enthralling as the Saga Norén chiller – indeed, this eight-parter is from the imaginarium of the co-creator of The Killing, Torleif Hoppe.

A happy Copenhagen cop gets a ferry, in a rancid storm, to Poland, with his infant daughter, to chase a child abductor. Leaves the pram on deck to be, briefly, seasick. Guess what? Cut five years forward: a once-happy Copenhagen cop chances on a crucial flaw in the Danish DNA database of offenders and curdled hope flutters into life. Four episodes in, I too am truly, appallingly, gripped by hope, and it’s also got Charlotte Rampling as the incroyably chic older French investigator.

Barely less captivating is The Same Sky, a Paula Milne creation for German TV, which rather disappeared into the maw of Netflix three years ago. Happily resurrected by C4’s sainted Walter Presents strand, it’s a genuinely exciting 1974 true tale, of a young East German “Romeo agent” sent west to honeytrap and pillow-talk an ageing single mother working for a western listening post atop Teufelsberg (Devil’s Mountain) in Berlin. Talking of Saga, this also has Sofia Helin as you’ve never seen her before: dowdy, lonely, old before her time, vulnerable. It’s hooksomely, toothsomely watchable: how swiftly recent history can become moral anthropology within a generation or so.

I was mystified by the new Sara Pascoe thing, Out of Her Mind, and can only conclude that I am of the wrong gender or cultural sensibility to review it. Relentlessly, scattily modernist, with tricks such as meta-references to its own sitcom-ness, the breaking of the fourth wall, the “real” Sara Pascoe commenting on the “fictional” Sara’s disaster of a life, it also felt very dated, just not in a good way.

Fictional Sara, who couldn’t seem to decide whether she was bitterly life-cynical about being dumped 15 years ago or childishly, naively, irritatingly self-obsessed and rude, had to cope with the twin outrages of her sister becoming engaged and her best friend being pregnant, apparently events on some manner of end-of-days scale. Cue some stock catty rudeness about rings, dresses, weight, pinkness. The real Sara, meanwhile, got on with making some decent points, albeit while rollerskating in a pink leotard, about, say, how advertising makes women feel inferior in order to sell them stuff or how fairytales offer girls false stereotypes, yet both points agreed on, surely, in the last decades of the last century?

The show is almost saved by Juliet Stevenson as the mother, utterly lacking in self-awareness: indeed, the entire supporting cast are strong, though I could have done with more Cash Holland. Yet such things have been done better, in the last couple of years alone, by This Way Up, Catastrophe, I May Destroy You, even Motherland… hence my mystification, because so often Pascoe, a wise author in her own right, is the wittiest thing going on any panel show.

‘A quasi-magical gift’: Count Basies, subject of Through His Own Eyes.
‘A quasi-magical gift’: Count Basies, subject of Through His Own Eyes. Photograph: AP

Some rather marvellous insights into the life of Billy James “Count” Basie snuck unheralded on to our screens, courtesy of a remarkable little film, Through His Own Eyes, from Jeremy Marre. It told the story of the boy from Red Bank, New Jersey, who went on to become one of the famous people on the planet, yet who managed to keep his private life remarkably unrevealed.

With grand access to interviewees and forgotten footage, it related seamlessly how the lad who stood in at 14 for an absent cinema pianist would achieve greatness. Aided only by a quasi-magical gift of understanding every wrinkle and flounce and offbeat and sway of what “swing” is – and it must help, too, when you have Lester “Prez” Young on tenor sax and Quincy Jones as your band arranger – he went on to become the first musician on the moon (Buzz Aldrin took the Basie/Sinatra/Jones ’64 recording of Fly Me to the Moon with him on tape).

Unshowy and even-handed, this also related how much he loved his daughter, Diane, born with cerebral palsy; yet she, hardly able to walk, able to speak, would become something of a muse to him. He wrote endless loving letters to her, talking about music, places, weather, blues – and 50 years on the road, on a hired Greyhound bus with the band, 48 weeks a year, that’s a shedload of letters. We heard how deeply he loved his wife, Catherine, yet how he was in the doghouse for much of his early life thanks to on-the-road, um, affiliations. Above all, we got a measure of the man, a bugger for gambling and the ladies yet unfailingly unpompous, controlling the band with a whip hand, yet a subtle and steady one, immensely popular with all his musicians to the end. I could have watched eight hours of this.