Personally, I have a theory, regarding... KATIE. Whatever she really is, she knew what the speck was from the beginning. After rewatching, she's the only other person in that scene with an 'Oh Crap' look when the speck first floats by. Everyone else is just bewildered at Horton's antics. But she looked like she knew exactly what was going on there. Especially with the last shot being her floating out of the Jungle of Nool and into the Void between all worlds, which are all revealed to look like specks of dust.
Dr. Larue, the doctor Mayor McDodd went to in order to find out what would happen to his floating speck of a world, starts to believe him later in the movie because of the unexplainable snow... yet does NOTHING when he's being ridiculed by the Council! She told him straight to his face that he was right about their world being in terrible danger, so why doesn't she step up and defend the poor man?
Maybe she was afraid of being ridiculed too?
Dr. Larue didn't have any proof that the mayor was right, either - she speculated that the existence of their world on a speck would lead to things like tremors and weather changes, but that doesn't mean the council would be any more likely to accept it as an explanation over her just getting worked up over nothing.
Vladd drops the flower into an endless field of flowers that all look identical. So why did Horton go through what was obviously an unrealistic task of finding that one flower with that one dust speck. No one else would have bothered. The speck was safer in that sea of flowers than standing alone on an easy vantage point on a cliff.
Horton was feeling protective of his tiny friends. He may have feared that Katie would later go find it and cause more harm.
They were just dropped from the height of a mountain. He probably wanted to make sure they hadn't died. Also, just before the clover was stolen from him the mayor was asking him to prove he existed; if he didn't find the clover again he's pretty much condemning his friend to look like a nutjob to everyone forever.
How exactly did Morton learn that Sour Kangaroo sent Vlad Vladikoff after Horton? (In the movie)
All versions of the story portray many of the denizens of the Jungle of Nool as loose-lipped yentas. It can be assumed that Morton heard it from a guy who knows a guy who knows a guy, etc.
In the climax, how did Kangaroo and the residents of Nool get to Horton despite the fact that he destroyed a bridge earlier, and the only way to get to Mount Nool was across said Bridge?
Maybe the bridge spans a gorge that actually closes itself up somewhere further to the left or right. Horton was in a hurry and may have thought he didn't have enough time to go around.
During the climax of the movie...The animals of the jungle are shown to be willing to listen when Horton claims to hear the Whos making noise, even though they can't hear it themselves. Why doesn't he just give someone the clover, go somewhere far away where he can't hear them, have them say something to it that he wouldn't know or be able to guess on his own, and then come back and have the mayor tell him what it was they said? Wouldn't that be sufficient proof that there were people on it?
It was too late. By the film's climax Sour Kangaroo had whipped everyone up into such a frenzy that there wasn't much Horton could do other than hold out until the Whos made enough noise to be audible. Plus, he's panicking. Perhaps if he had thought of that earlier it would have worked.
What exactly is Vlad Vladikoff's motivation? First he demands an exorbitantly high price—the Kangaroo's own baby!—but once she mentions hiring someone else he's so desperate for the job that he does it for free. What does he gain from any of this?
I think it's a matter of pride. Vlad is insulted when the Sour Kangaroo suggest she'll get the Wickersham brothers to do it instead. After all, monkeys aren't intimidating. Could be a [Batman Gambit] on her part.
It's made clear from the beginning that Jojo didn't want to become mayor of Who-ville. So what DOES he want to be? Judging by all the musical instruments in his observatory hideout and his singing voice, I think it's safe to assume that he wants become a musician or singer.
It's also possible he hasn't actually decided what he wants to be yet, he just knows he doesn't want to be mayor.