Grace Dent on TV: The Sound of Musicals, Channel 4

The dance routines! The insanity! The naked tanning sessions! That's showbiz!

Super trouper: Dickie Wood was filmed as he took over one of the main roles in ‘Mamma Mia!’

As this week's The Sound of Musicals beautifully illustrated, there's a strong argument that the biggest eccentrics in the world of showbusiness are stage-musical producers. Or more accurately “potential” producers of stage musicals. I watched this show, coincidentally, on the same day I was invited to American Psycho – The Musical, which opens at the Almeida, just before Christmas. Yes, clearly at some point a potential musical producer read the Bret Easton Ellis classic gore-fest and thought: “I know what will liven up these drawn-out necrophilia and cannibalism sequences! A lovely big dance routine! Maybe someone can pirouette on, juggling pieces of spleen. Then a torch-song number in act two where Patrick Bateman sits in a spotlight lamenting the woe of removing dried-in blood from a bespoke tie!”

My very favourite send up of musical land is Richard Curtis's first feature film The Tall Guy, with Jeff Goldblum, where failing actor Dexter King finds career salvation in the West End musical Elephant!, a joyous, ham-fisted romp about the life of Joseph Merrick (“The Elephant Man”) featuring dance routines around floating hospital beds and Goldblum doing “twinkle hands” with a sack over his head. Musicals are ridiculous. But they're supposed to be big, brassy, distracting slices of ridiculousness.

In the second episode of this Channel 4 theatreland documentary we watched established musical legend Cameron Mackintosh and first-time producer Amy Anzel driving themselves and dozens around them to the edge of sanity over their vision. Amy's dream, to bring Happy Days – The Musical to the West End skirted close – in a high-functioning, fabulous way – to the dictionary definition of insanity. Amy had pledged £30,000 of her own savings already, she had convinced Strictly Come Dancing's Craig Revel Horwood to choreograph and put his name on the front of the title –Craig Revel Horwood's HAPPY DAYS!. She had began recruiting a cast. She'd called in Chico, yes, he of Chico Time. And when Craig Revel Horwood ran for the hills wanting no more of Amy's Happy Days dream, did our heroine just roll over and give up? No, she did not. Because this is musical world. “No” doesn't mean “no”. Instead she became fixated on Henry Winkler, the Fonz, and sent him 14 emails asking him to be the producer. And when the Fonz blanked all of those 14 emails, did Amy give up? No, dagnammit, she did not. She ambushed him at a book signing. Eventually The Fonz said yes. Amy isn't even remotely unusual. There are people like her all over Soho right now running frantically between coffee-meeting and book-signing guerilla attacks, haranguing other people to help them put on their musical.

Of course, the dream beyond the dream is that one's “small, lovable musical with a big heart” turns into a thunder-musical behemoth like Mamma Mia!, which has been giving easily pleased tourists somewhere to shelter from the London rain for 14 years. Mamma Mia! is one of the most terrible musicals ever staged and I've sat through Jesus Christ Superstar at the O2. And Cats, right at the end of the 1980s West End run when the costumes appeared to have fleas. Mamma Mia! takes the incredible music of Abba and roughly tacks it around a Greek “who's my daddy?” plot. It's a good place to take your visiting Auntie Sheila from Cleethorpes and then maybe take some codeine and hope all the encores make it too late to visit Hamleys.

In this episode we watched 21-year-old Dickie Wood preparing to slot into one of the main roles of Mama Mia!, learning the lines, perfecting the dance routines and getting a fake tan, which Mamma Mia! seem to prefer to do in the old-fashioned way of letting a man rub the cream laboriously into your buttocks over the space of 40 minutes while you stand in front of lots of other men, naked. I might email Mamma Mia! and inform them of the invention of spray-tan booths which take 10 minutes, are private and let kids like Dickie keep their dignity.

Possibly worthy of a whole hour to itself was the coverage of Cameron Mackintosh's struggle to bring back Barnum, the circus musical with which Michael Crawford melted the nation's heart in the 1980s. Barnum was, back then, a massive deal. Crawford's skill and tenacity in the role of PT Barnum was considered almost superhuman. That said, it was the 1980s. There was not one scene of Barnum within The Sound of Musicals that inspired me to watch the 2014 tour with Brian “It's a Puppet” Conley. If I wanted to watch jobbing actors dancing with ribbons on sticks and juggling skittles, I'd move to Brighton.

As Mackintosh pushed forward with his plan to open Barnum at the Chichester Festival, the unavoidable fact was that the current PT Barnum, Christopher Fitzgerald, had only managed the song on the tightrope twice prior to opening night without falling off. The cast gathered backstage as he made his first public attempt. A massive cheer erupted when Fitzgerald succeeded. But reviews were lukewarm so he was soon dispatched back to America. That really is showbiz.