These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Crack Pairing: Eternity and Kismet fall in love over the course of the story. Seriously. For those of you who don't know, they are the living embodiments of the Marvel and DC universes, respectively. Incredibly, their embrace as Krona tortures them and their visible sadness when they are finally separated are actually pretty moving. Note that pairing them with anyone else but each other would be even more of a Crack Pairing.
Hawkeye and Black Canary are an item together briefly while the universes start to collapse on each other.
Superman is a Jerk Sue for most of the crossover, not The Cape as he's normally written.
Captain America was also written this way — it was given a vague explanation about the two heroes who were most closely tied to their own respective worlds being the most unnerved by the change in their accepted reality.
The universes also have differing physical properties. At one point, Superman comments that sunlight in the Marvel universe feels "greasy", which probably added to his irritation.
Dork Age: Leave it to Kurt Busiek to make a compelling story point out of these. In the third chapter, the heroes are in a happy Silver Age style two-earth universe, and once they finally realize that this is just a distraction as the Earths destroy each other, they ask to see the worlds the way they should be. Each character sees the Face Heel Turns, Heroic Sacrifices, Suspiciously Similar Substitutes, and With Great Power Comes Great Insanity that they will experience in the "correct" universe. They are horrified and initially consider the selfish idea of just leaving the Earths as is. Finally Hal Jordan, who arguably has the most to lose, tells everybody that they don't have the right to play God with the Earths (which, ironically, was the root of his own Dork Age), and the heroes agree to restore everything that was, both good and bad.
Prior to the 90s DC versus Marvel series, all other crossovers between the two companies were written as if the characters had always lived in a shared universe and been aware of the existence of the other company's locations and characters (the MST3K Mantra was in full effect). Avengers/JLA actually provides a possible belated explanation for this, as The Grandmaster's plan does indeed create a shared universe in which Marvel and DC characters are aware of each other and cross over regularly. Due to the nature of retroactive alterations in time, Superman vs. Spider-Man, Batman vs. Hulk, Teen Titans vs. X-Men and all the other prior crossovers can be seen as taking place in that alternate shared universe.
There is a pre-existing explanation for these crossovers: The Unlimited Access mini-series revealed that universes tend to temporarily fuse in "crossovers", not only in the present day but also in the past, so Access must travel in time to ensure the universes re-split after each crossover to prevent them from becoming the Amalgam Universe again, with everybody forgetting such crossovers after returning to their own universes (this miniseries also included a previous JLA-Avengers crossover between the founder members of both teams).
The Official Handbook of the Marvel Universe has numbered at least one Earth in the Marvel Universe (Earth-7642, to be specific) where the DC characters exist and regularly cross over with Marvel's characters; it's where Marvel canon places all of the crossovers aside from Marvel vs. DC and JLA-Avengers. The latter, at least, is implied to have involved Earth-616, the main Marvel universe.
HSQ: Pretty high for a mainstream superhero comic.
Thor hits Superman with his hammer, Supes catches it.
Krona defeats Galactus... And then builds a house out of him.
The Epic Battle scenes are pretty incredible too, especially for hardcore fans (one panel shows Superman going one-on-one with Count Nefaria)
Moral Event Horizon: Most of the villains Krona summons to battle the heroes are a bunch of dumb thugs. But Dreamslayer decides that Hawkeye and Flash are inspiring their friends with their good humor, and coldly disintegrates them with a magical blast. Don't worry, though. Dreamslayer and his associate Doctor Diehard get some Laser-Guided Karma courtesy of cosmic-powered Kyle Rayner. Theirs are the only graphic deaths in the story. It helps that Dreamslayer is a being of pure magic, and that Doctor Diehard is a robot.
One-Scene Wonder: The Thing only appears for two pages, but absolutely steals the show by just being his ever-lovin' self, rendering Batman speechless until he leaves. After this the stunned Dark Knight has to admit that Grimm has a "rough-edged charm" all his own.
Tear Jerker: Barry Allen and Hal Jordan have a quiet chat, discussing their successors, and wishing they could have one last picnic with their friends.