Big-Lipped Alligator Moment: The "Ooga Booga" number. It comes out of nowhere and doesn't do much besides confuse and annoy the three bystanders. In fact, the Grinch's laughter at the end suggests he did it for the sole purpose of amusing himself for about twenty seconds.
Foe Yay: "Will...will you please scare me some more, sir? I-I, I sort of like it." Well, Euchariah, that's certainly one way to stall the Grinch.
Nightmare Fuel: It goes without saying that the Paraphernalia Wagon sequences are this. And recall that the Grinch was going to unleash that on all of Whoville. For no other reason than the fact that the wind is making him grumpy.
There's also the Slasher Smile the Grinch gives at the title card, perfectly setting the mood.
The second to last part of the ending. Sure, Euchariah managed to stop the Grinch from going to Whoville to terrorize the Whos, but the Grinch points out to the audience that "that wind will be coming back someday. I'll be coming back someday," followed by an Evil Laugh.
The sinister music accompanying this scene hardly helps.
Tear Jerker: Max's song, oh boy. The fact that the Grinch at one point mocks him during it makes it even sadder.
How many times have I said and said,
How many times have I said in my head,
"What am I doing here?"
"Why am I the slave of this grinchy old crock?"
And I say "how I wish I could turn back the clock,
And have the fine future I had once before,
And again be an innocent puppy once more."
What am I doing here?
Doesn't matter much how,
But my dear old auntie Wolfie wouldn't, I fear,
Very much care for me now.
The Woobie: Dear God, Max. Like in most stories involving the Grinch, Max is usually portrayed as far more sympathetic than his master, but in this one, he is clearly not happy being stuck with the Grinch. You just want to hug the poor thing, and you really root for him when he decides to ditch the Grinch in favor of Euchariah.
Also, the flower that the Grinch intentionally crushes with his wagon wheel. It weakly tries to rise up as though it were sentient — and, given the nature of Dr. Seuss, probably is.