The Weekend's TV: Donald Trump: All-American Billionaire, Sun, BBC2<br/>American Dream, Sat, BBC2

He's still making hair-raising claims
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Is my hair OK? Nice and fixed?" asked Donald Trump at the beginning of Emily Maitlis's profile, Donald Trump: All-American Billionaire. Fixed, Donald, certainly but as to OK I think that's a matter of taste.

My wife walked past as I was watching and happened to catch a glimpse of the strange spun-sugar nest that sits on top of your head: "All that money and that's what his hair looks like!" she said, not recognising, I think, that this penthouse development might have looked even worse if less had been invested in it. "It is actually my hair... it's real," Trump insisted later when Maitlis raised the matter. But then Donald's relationship with the actual isn't always entirely dependable. "I call it truthful hyperbole. It's an innocent form of exaggeration," he once wrote about his tendency to stray from the strictly verifiable in his statements. Others would call it something less forgiving, including those who oppose his plan to develop a golf course near Aberdeen. He's repeatedly boasted to the press that 93 per cent of local people approve of his plans, a statistic whose origins he couldn't explain to Maitlis here and – despite a promise to get back to her with the details – his organisation couldn't either.

Donald may well genuinely believe that figure by now, since Maitlis's film made it apparent that his self-belief easily outweighs the niggling contradictions of the world at large. "If you're going to be thinking anyway, why not think big," runs one of his mantras, picked out on the wall of his Las Vegas hotel. The same principle applies to self-promotion. Indeed, he makes Mussolini look self-doubting, having learnt the hard way – during the property recession of the Nineties – that any kind of doubt can be fateful. At one point he was within 10 days of having to file for bankruptcy, bragging to associates that a panhandler on the street had $900m more to his name than he did. But he somehow persuaded the banks that they would lose more in sinking him than by backing him and made it through the squeeze. Now the Trump name is so closely associated with a brassy kind of luxury that he can make money by franchising it for "affordable luxury" (ties that allow ordinary Joes to fantasise briefly that they're Donald Trump).

His wasn't a rags-to-riches story, but a riches-to-even-more-riches tale, in which a bumptious young man from Brooklyn takes his father's successful building firm and invades Manhattan through sheer chutzpah. Briefing the architect on his first deal – in which he wrapped a well-located eyesore in gold-cladding and made a fortune – Trump told him: "I'm 25 years old and I'm going to be bigger than anyone in New York in five years' time." He'd acquired this bumptious self-regard, Maitlis suggested, at church, the presiding cleric being the positive-thinking guru Norman Vincent Peale, whose theology was light on humility and big on confidence. If you have trouble getting your camel through a needle's eye, Vincent Peale would suggest, don't give up... just go out and build a bigger needle. Trump has absorbed his teachings well. Arriving for a photo-shoot in the Scottish sand-dunes whose redevelopment has been so controversial, he grandiloquently announced that he'd renamed them the Great Dunes of Scotland, in honour of his mother and the people of Scotland. "We've had tremendous support from the environmental groups, so I'm very happy about that," he told the assembled press. Maitlis quietly pointed out that of seven environmental groups who'd given evidence to the planning hearing every one had been opposed to Trump's plans, though sadly she didn't seem to have had a chance to put this to the man himself. Not that he would have been punctured anyway.

The phrase "American Dream" came up several times in Maitlis's film – a deeply ambivalent ideal – somewhere between sedative and stimulant – which got sceptical treatment in the series of that name on Saturday night. The programme uses archive footage and home movies to illuminate its account of American social transformation in the last century, and this week it featured several people for whom the American Dream had been nightmarish. Some of them were still deeply bitter, including Toru Saito, a Japanese internee during the Second World War, and Russell Means, who took part in the Native American armed seizure of the town of Wounded Knee in 1973. But others, such as Betty Blakeney White, had successfully fought to make the fine rhetoric of the American Dream into a kind of truth. When she was a young girl, she was sexually abused by the teenagers she babysat for: "My mother's paying you and I can do anything I want to, nigger," said one of them. But a combination of the civil-rights movement and her own determination meant that she felt she'd made a success of her life in a distinctively American way.

The archive footage is wonderful, whether it's the home movies of gay dinner parties or the film taken by a travelling film-maker called H Lee Waters, who would visit a small town, film everything he encountered and then hold a movie show. "See hundreds of folks you know", his poster promised, and people flocked. His footage showed a Norman Rockwell idyll of small-town America, everyone smartly dressed and smiling and no one obese ("Because we walked everywhere there weren't any overweight people," someone explained). The interviews reminded you that behind that dreamscape lay a lot of nightmares.