The ad-lib lyrics! Cases in point: Joshua Tree tour, 1987, Denver. During Gloria, Bono accidentally drops his mic and instead of singing "oh lord, loosen my lips" he sings "oh lord, strengthen my grip."
But there are hundreds of examples. The location-specific section in Out of Control where Bono talks about their early experiences in that town. In Denver he talked about playing The Rainbow Music Hall back in '81, for example.
Of course, there's always that moment when they walk on stage and you hear the electronic sizzle and pop of Edge plugging in his guitar.