During a rare quiet moment in Lady Gaga's idea-splurging, two-hour show, the singer sits at a keyboard mounted on a motorcycle and talks about a record executive who suggested that her Born This Way album catered too solicitously to her fanbase's "weirdos and freaks". "They called it a niche," she says, triumphantly surveying the 55,000-strong crowd. "This is a big fucking niche."

It's crucial to Gaga's self-image, this idea that she can be both fantastically successful and an arty subversive catering to a tribe of outcasts. Whether or not you believe that, she certainly does. The problem is squaring this rhetoric with the pragmatic demands of stadium pop. Just as her records cleave to reliable templates – Madonna, Bruce Springsteen, European trance-pop – her show ticks some familiar boxes.

So there's an expensive set constructed like a castle, enabling her to perform from various turrets as if she were Evita on the balcony. There's a squad of formidably buff dancers with whom she can flirt and grind. There are costume changes ad infinitum. And, inevitably, there is a half-baked concept that seems to involve the show taking place in a Government Owned Alien Territory (dancers wave black flags reading GOAT) prior to Gaga invading Earth and inventing a new, utopian race – although it's hard to say for sure, or indeed care.

Still, there are frequent moments of chutzpah and high-wire ingenuity. For Heavy Metal Lover she moulds herself into a cyborg motorbike and invites one of her dancers to ride her. Before Born This Way's stampeding title track, she emerges from between the legs of an inflatable pregnant version of herself, as if to say: match that, Madonna.

At times, performing in a face-obscuring insectoid helmet or banging on about GOAT, Gaga risks getting lost inside the spectacle, so the weakest part of the show is also the most revealing. Donning a fan-made T-shirt, she plays a peculiar new song about Princess Diana and Amy Winehouse called – brace yourself – Princess Die, followed by John Lennon's Imagine. It's both horribly embarrassing and endearingly sincere: a real departure from the stadium script that proves the gawky outsider line is more than just shtick. Likewise her decision to spend the hair-metal encore dancing with the kind of oddball hardcore fans that security guards are usually paid good money to keep at a safe distance. The tightly choreographed hits sound terrific, but it's when this curious star sabotages the slickness that she seems most herself.