Andrew Graham-Dixon bigs up The Secrets of the Mona Lisa (BBC Two, Wednesday) with the grand promise that his hour-long film “will change everything we thought we knew about the world’s most famous painting”. It’s a big claim and a generous use of the word “we”.

For most of us Leonardo da Vinci's 500-year-old portrait has become a tick-box cultural experience: see The Last Supper in Milan, visit Gehry's Guggenheim, get in line at the Louvre . . . You get the picture. Mona Lisa is like a film star: smaller in real life than you expect and impossible to get a good look at, because of the crowds in front of you taking selfies.

But a lot is known about the painting, it being the subject of a great deal of academic research. Graham-Dixon is terrific at demystifying art-appreciation jargon, and his film unfolds as a gripping art mystery with a satisfying revelation at the end.

There has long been speculation about whom the portrait shows. (It could even be a man, says Graham-Dixon, eyebrows arched.) The original Lisa was, it’s widely believed, Lisa Gherardini, wife of a cloth merchant, Francesco del Giocondo, who lived across the road from Leonardo’s father, and we visit the street in Florence where they lived (and later pass through Moscow, Singapore and Paris: this film wears its healthy budget well).

There's also the tantalising notion that another version exists somewhere. Leonardo is known to have painted multiple versions of many of his paintings, so why not of this portrait? The problem for art scholars has been that the Mona Lisa in the Louvre doesn't sound like the picture described by someone who saw Lisa's portrait in the artist's studio. For one thing, she had bushy eyebrows; the Louvre one doesn't.

So other Mona Lisas pop up from time to time. Graham-Dixon tracks down two. One is owned by anonymous financiers who have a Mona Lisa locked away in a vault in Singapore. (It looks like a Mission: Impossible set.) There's another in Russia; to see it, the film crew travels to Moscow, where they wait to be told its location. After much cloak-and-dagger stuff, appropriately enough, it's in the old KGB headquarters.

The big reveal – literally – comes at the end, in Pascal Cotte's studio, where the French physicist turned art expert shows how, having been given access to the Louvre's Mona Lisa, he has spent 10 years testing it, using his layer-amplification method to "reveal its layers like an onion". What he and his camera have found – watching him reveal those layers is fascinating – is that another woman's portrait lies beneath the one we see. She has an elaborate headpiece, bushy eyebrows, a bigger head and a smaller, firmly-set mouth – definitely not the enigmatic smile of the Giaconda we know.

Cotte and Graham-Dixon theorise that the painted-over portrait is that of the merchant’s wife, while the one we can see in the Louvre is the artist’s idealised version of the woman. It sounds convincing, and a satisfying end to a compelling documentary – until the next theory about the world’s most famous painting comes along.

Ireland’s Rising (RTÉ One, Sunday) is an accessible introduction to the onslaught of 1916 commemorative programming coming our way. The series sees Anne Doyle, Jim McGuinness and Fiona Shaw, among other well-known people, go back to their home places to discover rural connections with the Rising.

So getting the Dubliner Ryan Tubridy to present a Connemara story seems a bit of a cheat, but his credentials are shown early – local historians tell how his great-grandmother Jane, a schoolteacher, corresponded with Roger Casement about the poverty in the area – and the story of Volunteer activity in the run-up to the Rising goes from here. It also works because Tubridy is obviously passionately interested in Irish history and has an appealing, quiet way of communicating that interest. It’s quite different from his chatshow persona.

Another thread to Ireland's Rising is to stress local interest in the event, so it feels as though there's an element in this TV taster of saying that, honestly, the media haven't made this up: people up and down the country really are engaged with the idea of the commemoration.

So when did you lose faith with London Spy (BBC Two, Monday)? The star-packed contemporary spy drama started out so well: a beautifully filmed spooks mystery with a stunning cast, led by the mesmerisingly good Ben Whishaw as Danny. The first episode was one of the strongest openers in a drama this year, but five weeks later it ends bulging at its visible seams with every corny spy cliche in the book, a fantastical series of events unmoored from any believable reality.

In episode four we found out the (disappointing) answer to the mystery at the heart of London Spy: Danny's genius boyfriend, Alex, had invented a truthometer. This week we learn that the secret service killed Alex – while his mother, Frances (Charlotte Rampling), looked on – by suffocating him in a suitcase because of the consequences for world leaders were his "end-of-lying" algorithm to be let loose. No sense can be made of that sentence.

In the final scene Frances and Danny – who have spent the series barely hiding their mutual contempt – jump in a car and rev up, ready to take on the establishment like Scooby-Doo and Shaggy. “Let’s burn them down for real,” says Frances, in a line of dialogue as stilted and ludicrous as the final two episodes.

The most eye-popping TV programme this week, of course, is RTÉ Investigates (RTÉ One, Monday), which looks into the suspect practices of some county councillors. In the blanket coverage the following day, as people struggle to describe it, TV references multiply. There's Killinaskully, Father Ted and Ballymagash (from Hall's Pictorial Weekly). Joe Duffy on Liveline refers to the Monaghan councillor Hugh McElvaney using "the Homeland defence". For those not watching the fifth series of Homeland (RTÉ2, Tuesday), why not? With a plot about an Isis attack on a European city, it's chillingly good. (Duffy is referring to last week's episode). The CIA's Berlin chief, Allison Carr (played by Miranda Otto, a stand-out star of this terrific series), has been caught spying for Russia, but with a spot of quick thinking she turns the tables, saying that she is really the hero, that it was her Russian contact who was the spy feeding her intelligence.

And, unlike the councillor, in a plot development I’m struggling to believe, she seems to have gotten away with it.

Ones to Watch: Luther gets gruesome, Baz finds his roots

The police procedural Luther (BBC One, Tuesday) is back, with a vile, unnecessarily gruesome and graphic two-part story about a serial killer on the loose in London. You have been warned. The swagger of Idris Elba as the eponymous detective (right) doesn’t make it more appealing.

The Emmy winner Baz Ashmawy sets out to explore his Muslim heritage – a religion he was born into but has never really engaged with – in the two-part Baz: The Lost Muslim (RTÉ One, Tuesday). Seeing the religion through his eyes and those of his Egyptian half-sister, Mahy, should be enlightening.

tvreview@irishtimes.com