Television choices: David Threlfall puts the past to bed in a cracking cop drama What Remains

TV pick of the week: What Remains

Sunday 9pm BBC1

Never mind Peter Capaldi's transformation from Malcolm Tucker into Doctor Who: the harder thespian re-invention is for David Threlfall, Frank Gallagher in Shameless for the past 10 years, to persuade us that he is anything but a feckless poet of the Mancunian gutter. With a rough-and-ready haircut, but the same bar-room pallor, he makes a great start in this cracking new four-part drama by Tony Basgallop, a whodunit in which Threlfall's edge-of-retirement copper DI Len Harper investigates the death of a young woman whose mummified remains have been discovered in the attic of an apartment house. Russell Tovey, Steven Mackintosh, Indira Varma and David Bamber are among the residents and suspects.

America's Stoned Kids

Saturday 9.10pm BBC2

Denver, Colorado, is known as the Mile High City thanks to the nearby Rocky Mountains – and not because this conservative state has legalised marijuana. John Marsden, a psychologist specialising in addiction, visits Denver, where pot-smoking is more socially acceptable than alcohol, but parents worry that it's one giant experiment with their children's well-being.

Horizon: Dinosaurs – The Hunt for Life

Monday 9pm BBC2

A look at the research of Dr Mary Schweitzer, who found soft tissue and red blood cells in the fossilised bones of a 68- million-year-old T-rex, a breakthrough that led to "Jurassic Park" headlines. Now the palaeontologist believes she may have found traces of the creatures' DNA, and that dinos may be related to (wait for it) chickens.

Ancient Greece: the Greatest Show on Earth

Tuesday 9pm & 2.30am BBC4

Classicist Dr Michael Scott (Who Were the Greeks?) begins a series about Ancient Greek theatre, their greatest legacy alongside democracy. With performers wearing masks and a chorus commentating on the action, the plays tended to be a reaction to real events, says Hunt, who begins in Athens with Euripides, Aeschylus and Sophocles.

Martin Luther King and the March on Washington

Wednesday 9pm BBC2

"Tell them about the dream, Martin," urged the gospel singer Mahalia Jackson as Martin Luther King prepared to end his oration at the March on Washington for Jobs and Freedom 50 years ago today – thus prompting one of the greatest speeches of all time. This film looks at the background to the historic civil liberties march of 28 August 1963.

Burgled

Thursday 9pm Channel 4

Want to know how to protect your property? This Cutting Edge documentary following West Yorkshire Police in their fight against burglary in one of the worst-affected cities in Britain, Leeds, has all the latest innovations in crime-prevention. Offenders also offer their pennyworth – at heart they're a lazy lot, so even the simplest precautions seem to deter.

The Hollywood Complex

Friday 9pm PBS America

This slyly revealing documentary focuses on the Oakwood apartment complex in Hollywood that houses star-struck nippers and their parents as they gather for the television "pilot season" – the likes of seven-year-old Savannah, hoping for a bit part as a dying child in Grey's Anatomy. There's a scene where her mother suggests Googling "dying children" for tips.