It was some combination of allergies, overuse, and cigarette smoking, really. I would say that his voice on PopMart was generally better than it was on Elevation (I literally can't make it through the Boston DVD because of his voice), but it had its ups and downs. Mexico City was a really good night as far as the tour went. The opening night in Vegas, his voice was going crazy... at some points, it was brilliant, and at other points, it was abhorrent. The Las Vegas air and heat really screwed with him.
Sarajevo was by far the most interesting point of the tour, which makes the concert all the more special. Bono woke up that day sick, and without a voice. He drugged himself up at the start of the show, and sounded fine at first. The amount of power he put into Gone was incredible... then Real Thing came, and he seemed to blow his voice out doing some insane falsetto work on the "take me higher" part. Things started to fall apart in LNOE. By the time they got to Pride, Bono just mumbled out the verses, and let Edge belt out the chorus. Bono apparently got himself drugged back up after that to patch through, but his voice was still pretty awful through the show. He couldn't manage the chorus of Streets, so he sang it much lower than usual, while Edge sang it normally. Edge and Eno had to patch him through Miss Sarajevo, which was a total disaster for more reasons than that. I read somewhere that they were actually planning a full-band SBS that night, but Bono couldn't handle it, so Edge came up with his solo version right there, but I'm not sure if it was true. And then there was the beautiful version of One... Bono apologizes for his voice, gives a really nice speech about Sarajevo being the "city of the future", and sings the Hear Us Coming verse much lower than usual... all of which seems to add to the song.