First and I think foremost, Iran. Trump somehow manages to create a situation where he talks about Iran, Rouhani replies, and most of the world including America's western allies is left figuring that Iran is basically the adult in the room and has the right of it. Of course, America is better than Trump, whereas the real powers in Iran are rather worse than Rouhani, so that exchange doesn't mean those allies would side with Iran over the US or anything... but still. That's not a situation he should be in. Additionally, the absurd and blatant hypocrisy of blaming only Iran for crimes which Saudi Arabia and other American allies are equally or more guilty of, rather undermines the high ground he takes in various other parts of the speech.
Then, Venezuela. Now it's pretty obvious to anyone with a brain that Venezuela is an atrocious mess and Maduro is a disaster, so no issues here with harsh words against them - but given that Trump somehow managed to threaten military action a while back, making the rest of the world recoil in horror and giving Maduro one hell of a propaganda present, phrases like 'we are prepared to take further action' become a little scary. And as for 'The problem in Venezuela is not that socialism has been poorly implemented, but that socialism has been faithfully implemented' - no. Just no. Leave the right-wing talk radio shtick at home when you're speeching at the UN.
And then let's not forget the 'Major portions of the world are in conflict and some, in fact, are going to hell' line. Come again?
I will say, having read through the whole transcript now, that there's also more good stuff in there than I was expecting - the good stuff doesn't get as much press attention, I suppose. But that's the way it works - that's why you want leaders who carefully craft their speeches in a way that will draw press attention to the parts that they most want to publicize, and will make them and their countries look good. Trump certainly wasn't short on lavish and (in most foreigners' eyes) exaggerated praise for himself and the US - but blowing your own horn too blatantly isn't usually the best way to make yourself or your country look good.