Hollywood has a problem with films about South Africa and apartheid.

The opportunity to take a firm stand against a distant, obviously egregious racist system — and then bask in undeserved praise for courage, conviction etc — plays to the worst instincts of the film community. It usually leads to very bad films.

Invictus is not a very bad film. But it is probably the worst film Clint Eastwood has made since he started directing three decades ago.

The subtlety, the sense of humour, the toughness evident in films like Gran Torino and Unforgiven are all absent. Instead, this stiff hybrid biopic and underdog sports film, centering on the 1995 rugby World Cup and Nelson Mandela’s brilliant, brave efforts to unite a divided people around the game, overdoses on sugar and shmaltz.

The title (it means unconquered in Latin) refers in part to the poem by William Ernest Henley with its famous last lines, “I am the master of my fate, I am the captain of my soul”. Timothy McVeigh, the Oklahoma City bomber, famously chose it as his final statement before his execution in 2001. But it was also a poem treasured by Nelson Mandela during his 27 years of imprisonment at Robben Island.

It is almost impossible not to be stirred by the film|

The film starts with Mandela — impersonated with uncanny accuracy by Morgan Freeman — leaving that prison on his way to take up his presidency. You quickly see how hard his job is going to be when his bodyguards from the ANC, led by perpetually angry Jason Tshabalala (Tony Kgoroge), all but refuse to work with the Afrikaner special branch officers of his official security detail.

Mandela forces them to integrate, and over the course of the film you see both sides begin to treat each other with respect and eventually with affection. The key to this process, and to the much larger national process it symbolises, turns out to be Mandela’s decision to not abolish the Springbok rugby team but to adopt it and promote it.

Given that the national rugby team was so closely associated with the apartheid regime that black audiences cheered its foreign opponents when they came to play, this was a daring and clever move.

Mandela, a former athlete and a man with a profound understanding of the Afrikaner psyche thanks to his years in prison, takes a personal interest in the improvement of the extremely weak team. He begins by inviting its captain, Francois Pienaar (Matt Damon, suitably bulked- up, blonded and sporting a shaky Afrikaner accent) to tea. Pienaar is, understandably, enormously impressed by his new president and works hard to make the Springboks a truly national team in the lead-up to the World Cup.

Unfortunately the filmmakers display only the haziest understanding of the basic facts of South African politics, especially given that the film was shot there. For one thing, they give the impression that all white South Africans are Afrikaners. And not only are they seemingly unaware of the existence of the English South Africans, they also do not seem to know about the country’s “coloured” and Asian populations.

Moreover, you would never know from the way the apartheid past is dealt with that there were whites not only in the anti-apartheid movement but in the ANC, and that there were many blacks working for the security forces of the old regime.

All of this is shame because by implying that Mandela is merely dealing with a simple, American-style, black-white equation, screenwriter Anthony Peckham and director Eastwood make his challenge smaller than it actually was.

That said, there are a couple of moments when you get some sense of the scary, gangsterish edge of some ANC elements. There is even a hint of the price paid by Mandela’s largely estranged family for his extraordinary achievements, though it is hard to imagine any accurate film that would not make the man look like something close to a saint.

While Invictus too often patronises its audience by massively oversimplifying South Africa’s politics, it also falls between two stools in its depiction of rugby. Anyone unfamiliar with the game would certainly not come out of Invictus with any sense of its rules or scoring; anyone who knows rugby well may be surprised at the film’s inability to convey its excitement. Instead you get lots of pumped-up impact sounds and strange gurgling noises from the scrums.

Even more problematic, while both Francois Pienaar and Mandela agree at tea in Pretoria that the key to leadership is setting an example, there is no evidence on screen of Pienaar inspiring his team, just a lot of shots of Matt Damon looking thoughtful and a bit gloomy. There is of course an inevitable montage of the Springbok team training hard but their dramatic improvement remains inexplicable. Despite all this, and despite the fact that there is scarcely a subtle or unpredictable moment in the whole film, Invictus works. Indeed, it is almost impossible not to be stirred by it.

The film’s air of self-congratulation, the ghastly music (including an Eastwood-penned song called Colorblind), and civics-lesson scenes of the screenplay somehow cease to matter thanks to Freeman’s inhabitation of Mandela and the huge, inspiring power of the underlying true story.