In its own, strange way, it's kind of touching to see Beavis and Butt-Head bonding somewhat with the two drifters heavily implied to be their fathers. Even if none of them make the connection that they're related.
Sure, it's tacked onto the end of the movie and presented as almost an afterthought to all the insanity that preceded it, but when the boys show up back in Highland, accidentally find their stolen TV, and nearly cream their pants with happiness, it's definitely a great moment.
Beavis bonding with the old lady on the plane. Although they both have different ideas as to what their conversations are about, the woman does seem to find Beavis to be pleasant company.
A possible off-screen moment of heartwarming. When the plane takes off, Beavis has what appears to be a panic attack, and starts shrieking "We're gonna die! We're all gonna die!" Presumably, it was the kindly old woman sitting next to him who eventually got him to calm down, considering that in the very next scene, he's fine, and they're just making conversation.
Beavis in his Cornholio persona becomes pretty chummy with some of the world leaders at the White House conference.
Butt-Head's rather adorable initial reaction to seeing the pretty flight attendant. He doesn't look aroused, or even flirtatious- he looks positively lovestruck, with little red hearts floating around his head when she offers to help him fasten his belt. His reaction to this, after sitting in silence the whole time? A subdued, awestruck "I love you." Yes, Butt-Head can be cute.
Butt-Head's attempt to flirt with Chelsea Clinton was pretty cute, as well. "I noticed you have braces. I have braces, too."
In a really twisted way, Beavis and Butt-Head laughing when they see two vultures having sex. Even when they're dying of dehydration in the middle of the desert and relatively quick to accept their own deaths, they both manage to find something to laugh about.
When both of them are dying, Butt-Head's life flashes before his eyes. All he sees is his entire life of sitting next to Beavis on their decrepit couch, both of them laughing, as they age up from infants to teenagers. Butt-Head's response? "Woah... my life was cool!"