As Batman and Superman are fleeing from Metallo through Gotham's sewers, the two of them pass the time and distract from their situation with dissonantly conversation and snarky jibes. The whole sequence is hilariously dissonant, and provides a few of the funniest moments of the story.
One said conversation that made it into the movie, as Batman is lugging a Krptonite poisoned Supes around.
Superman: "You know who I was thinking about the other day? Magpie."
Batman: "The criminal?
Superman: "Do we know another Magpie? What ever happened to her?"
Batman: "Clark... what the hell are 'good villains?'"
And one that sadly didn't make it into the movie after Alfred confronts them in the sewers, made even funnier because Superman has just been electrocuted as well as poisoned and is barely conscious, yet still manages to get a joke in.
Superman (weakly): Your butler guards the Cave with a shotgun? You didn't have a spare Mr. Freeze Ray gun he could use?
Batman: This coming from a man who uses a dog with a cape to protect his fortress....
Everything involving Hiro and Power Girl. From the first gag, where they need to stall him for a while (omitted from the movie). Someone asks rhetorically how they can stall a thirteen year old supergenius, and then the panel clips over to Power Girl (with particular emphasis on her chest).
Lex Luthor calling Amanda Waller a bitch after she gives Batman and Superman the information they were searching for to stop the meteor.
When Superman and Batman are in the Batcave discussing Metallo's death among other things Superman says that Batman was there when they fought and would vouch for his innocence. Batman just gives him a "Seriously?" look because, well, he's Batman. The look itself is just hilarious and has to be seen to be believed.