There is quite a lot about Cradle to Grave (BBC2, Thursday, 9pm), the BBC's new comedy set in the 1970s, that is absolutely right. The colour is right: all those oranges and browns (the whole world was orange and brown in the 70s). And the sound: that old brr-brr of phones, the crackle of music on vinyl, as well as the sound of old men bellowing sexist, old-fashioned attitudes and young people challenging them. It reminded me that the 1970s was the decade when we started to learn how to be modern and the 1980s was the decade when we were forced to be.

However, there is also something slightly wrong with Cradle to Grave. It is based on the memoirs of the broadcaster Danny Baker, who grew up in Bermondsey in the 70s and at times it is funny – even very funny – but we've all lived through the teenage experience and we've all seen it told over and over again on film, on television and in books. What's new about this one? What's different about it?

The answer is not much. The period detail is spot on (as it always is with the BBC) and there are some amusing reminders of what it was like to live in the 70s (I think I'd forgotten that we used to rent televisions until I watched the sequence about Radio Rentals). But there's nothing original or arresting about the teenage experience, or even the teenage experience in the 1970s. Peter Kay as Danny's father does his familiar comedy turn - colourful, grotesque, large, as if he's been drawn by Loony Tunes - but the coming of age story came of age a long time ago with Adrian Mole. It's absolutely fine to take the subject on, but you have to do it a new way – doing the 70s nostalgia turn will distract us for a few minutes, but then we'll sit up and notice one awkward fact: this story has been told a hundred times before.

The story in Boy Meets Girl (BBC2, Thursday, 9.30pm) is less familiar, although not uncommon – there was a transsexual character in Coronation Street for a long time, but more recently, an older trans character was the star of the American series Transparent and Eddie Redmayne is about to play Lili Elbe, one of the first people to undergo gender surgery, in the movie The Danish Girl.

Boy Meets Girl has taken the subject a stage further by casting a trans actor, Rebecca Root, as the central character, which raises an interesting question about casting roles in film and television. Redmayne was lauded for playing a disabled man, Stephen Hawking in The Theory of Everything, and there's already talk about him winning an Oscar for his trans role, but is it right? There's a growing body of opinion that only disabled actors should play disabled roles and only trans actors should play trans. It's the same argument that put a stop to white actors playing black roles, but who really likes that kind of tyranny? Choose the best actor for the role and get on with it.

The actual story at the centre of Boy Meets Girl was engaging enough – in fact, it touches on the same territory as Cradle to Crave ie. young people trying to find a date – although, in the first episode at least, the entirely relaxed attitude that everyone takes to the trans issue was unconvincing. Recently, hundreds of students walked out of a high school in Missouri over a trans girl's request to use the girls' locker rooms, prompting the girl, Lila Perry, to say this: "It wasn't too long ago white people were saying I don't feel comfortable sharing a bathroom with a black person and history repeats itself." It proves, and there are many other stories like it, that prejudice is real and widespread and I hope that in later episodes Boy Meets Girl tackles that fact. If this comedy-drama is going to take on a real issue, then it also needs to convince us that it is living in the real world.