Smash, Sky Atlantic, Saturday / The Bridge, BBC4, Saturday

Saturdays have got sillier with Sky Atlantic's new and curiously dated series set on Broadway

Are you looking for something a bit different on TV for Saturday nights? Are you sick of audition shows in which mildly talented singers stand on stage and belt out "You Got the Love" at four chair-backs or (worse) David Walliams? Do you sometimes wonder if there's anything more interesting happening on Planet TV than Simon Cowell telling a palpitating septuagenarian chanteuse, "You're a little tiger, aren't you?"

Try Smash on Sky Atlantic. Steven Spielberg has been working on it for three years and executive-produced the pilot, which cost a reported $7.5m. The first scene is an audition, at which a pretty girl in a sparkly blue frock is singing "Somewhere Over the Rainbow". Just as you think you've tuned into The Voice, a mobile phone rings and the audition director chats to a friend while flapping a hand at the appalled ingénue and saying, "That was fine. You can go."

Instantly, we're pitched into the world of Broadway – the passion, the tears, the tits, the bitching, the hot lights, the hot sex, the competition, the waistcoated piano man, the jazz hands, the five-six-seven-eight-and-twirl – as we follow a gang of flappy egoists striving to launch a new musical on the life of Marilyn Monroe.

The 15-part series, created by Theresa Rebeck, comes at you like the Hot Box Girls in Guys and Dolls. It embraces all the clichés of musical theatre like old friends. "Being in the chorus is like being a nobody," laments busty trouper Ivy Lynn, still hoofing in ostrich feathers after 10 years. "I'll see you in court!" grates tough-bunny producer Eileen (Anjelica Houston) to her husband, who's been (you'll never guess) shagging starlets. "Sometimes dreams are hard," complains dewy-eyed Karen from Iowa to her uncomprehending parents. "I felt happy just being backstage," breathes Ellis, a creepy young hanger-on, "It felt like – home."

This showbiz schlock sounded tired around the time of Broadway Melodies in 1936. It sounds positively weird when bandied about in contemporary New York, where an audition filmed on a smartphone can be all over the web in hours. Luckily, to keep us grounded amid all the emoting, we get Debra Messing, from Will and Grace, at the centre of the action. A fine comic actress, she plays Julia, who's trying to write the Marilyn musical with her gay composer chum, Tom. Tom is full of camp outrage and puts his head on one side to suggest cute horniness – in other words, channelling Jack from Will and Grace, circa 1998.

The show boasts two British actors, Raza Jaffrey as Dev, an improbably high-flying Brit at the mayor's office who's courting Karen, the Iowa ingénue; and Jack Davenport as the maverick, Cockney-sparrer director who's (incredibly) brought in to drill an American cast in evoking the life of an American idol.

There was one excellent baseball-themed dance routine and a nice conceit of having the rival girls sing while emerging from the Times Square subway, past oblivious passers-by. But whether we'll be able to stand 14 more weeks of this old-fashioned hokum, I doubt. (Sob!) But perhaps I've been too rash! (*Worried frown*) Should I give it another chance? (*Sings* "I don't know how to laahhhve him ....")

If you're still bored by your Saturday night, tune into the new Nordic crime thriller, The Bridge. The title on screen is Bron/Broen (i.e. "bridge" in Danish and Swedish): the murder investigation involves the police of both countries after a corpse is found lying on the border. With shocking literal-mindedness, the killer has slashed the victim across the middle – and the lower half not only doesn't match the upper, it's been deep-frozen for a year.

Handling police inquiries on the Swedish side is Detective Saga Noren (Sofia Helin), a tall, beautiful ice maiden in tight leather trousers. From the Danish side comes her polar opposite, Martin Rohde (Kim Bodnia), lazy, unshaven, roly-poly, flirtatious with secretaries and given to bending the rules. The writers have tried hard to give them extra "character" to distinguish them from other Scandi-cops. Martin, having just had a vasectomy, clutches his groin a lot and cannot sit down. Saga appears to be autistic. She's emotionless when confronted by a woman hurrying to get a replacement heart to her dying father. She doesn't see how presenting an official complaint against Martin might just slightly damage their relationship as partners.

But I expect you want to know about her jumpers. She doesn't have any. She wears T-shirts, which she blithely removes at her desk before wriggling into fresh ones taken from a drawer, while the men in the vicinity try not to gaze at her bra.

It's a fresh idea, to have a female cop with no insights at all into how others might feel. But then this is a superior cop show, with a running theme about communication: how Danes and Swedes struggle to understand one another's language and accents; how different age groups tell each other off for using redundant slang. The palette is all washed-out pale greens and pinks among the 40 shades of Scandinavian beige, classily photographed by Jorgen Johanssen. And the plot is genuinely exciting. The first episode ended on a nail-biter, as an unpopular journalist found himself imprisoned in his car with the windscreen wired to a ticking bomb, while the glacial Saga grilled him by phone about his religious beliefs. I may have to come back for more, if only to establish just how many T-shirts Ms Noren keeps in that drawer.