My view of Howl is that the first lines are the introduction to the first part, painting an image with a broad brush, and that the next follows on in more detail. In fact, we can take all of Part I as commentary on its subjects' actions, which means that we can actually figure out a lot of what those best minds did. Most of them were Beat poets or members of the rising counterculture tide that swept across the country in the next decade or two. Here are just a few:
who jumped off the Brooklyn Bridge
That would be Tuli Kupferberg, a fellow Beat poet and artist who jumped off the Manhattan Bridge in 1944 at the age of 21. The idea that it was the Brooklyn Bridge was perpetuated in part by Ginsburg.
who sang out of their windows in despair, fell out of the subway window . . .
This entire section (and beyond) refers to Bill Cannastra, who awkwardly jumped out of a subway window for reasons involving liquor and died by decapitation. Cannastra was energetic, a drinker, a partier, and extremely smart. His death and his personality are referenced in the writings of several Beat poets, including John Clellon Holmes and Jack Kerouac.
who went out whoring through Colorado in myriad stolen night-cars, N.C., secret hero of these poems, cocksman and Adonis of Denver . . .
This is Neal Cassady, a Beat poet and close friend of Jack Kerouac, known for his extensive drug use. It may have led to his death, in 1968. Cassady was viewed similarly to Cannastra, and their deaths while still young (though Cassady died much later) drove this home.
who threw potato salad at CCNY lecturers on Dadaism. . .
This incident pertains to Carl Solomon, who strongly influenced and inspired the poem (including Part III). His psychiatric problems in particular and Ginsberg's reactions to them play a large role in this part, and of course show up earlier. Solomon's actual madness is seen again in the collective figurative madness of the rest of the Beat Generation; his suffering is their suffering.
There are plenty of other allusions to real-life incidents and people - these are only a few. The entire group was largely composed of the artists and writers and poets that Ginsberg knew firsthand, or through other friends. They collectively make up the "madness" that Ginsberg saw - in particular, in Solomon. He feels that he sees the madness and destructive tendencies in all the artists and poets and non-conformists around him. The point, though, is that he is attributing the madness to the societal conditions of the time - which is what Howl is all about!