During an otherwise moving discussion over sending their newborn son to Earth, Lara mentions her fears that the humans will kill Kal-El upon discovering what he is. Jor-El, in honest befuddlement, asks "How?"
Zod's reaction to learning Kal-El was conceived naturally and without any specific design: "HERESY!" It's Michael Shannon's delivery that makes it entertaining.
Clark rips a burning oil rig's door open to save the workers trapped inside. The workers are quite puzzled at first when seeing their savior, who's fireproof and shirtless.
When Lois arrives at the US military's post in Canada investigating Kara Zor-El's scout ship. Clark, going by "Joe," is tasked with collecting Lois's belongings, and Lois tells him to be careful because they're really heavy. Clark has every single one of her bags slung on his arms, clearly unhindered by their weight. Lois stares for a moment and then gets right back to work.
When Colonel Hardy shows Lois her "room" at the base, she turns to him and asks, "What if I have to tinkle?" It's not just her choice of word; it's also the sweet, girlish tone (and smile) with which she delivers the line.
And then Hardy tells her there's a pot. In a similarly innocent tone.
After informing Lois that he's going to cauterize a wound given to her by a robot in the Kryptonian scout-ship, Clark gently orders her: "Hold my hand. This is going to hurt."
Lois: What's the 'S' stand for? Clark: It's not an 'S.' On my world, the symbol means "hope." Lois: Well, here, it's...an 'S.' (beat) How about Sup- (static)
Up until Superman gets serious, the entire interrogation sequence, especially when Supes talks to the people on the other side of the one-way mirror. Before casually mentioning that the people furiously loading tranquilizer guns in the room behind them, don't need to bother.
Speaking of casually, the manner in which Clark/Superman separates his handcuffs before addressing General Swanwick is funny in itself.
Clark's general approach to things, separating his take on The Paragon from the other iconic comic paragon (see Steve Rogers in Captain America: The First Avenger); seeing as he's still trying to find his footing, his very straightforward and rather blunt approach makes him just as awkward in moments as Steve is, but in his own way.
Superman about to lift off, which generates shock waves:
Superman: (to Lois) You might wanna step back a little bit. (beat) Maybe a little bit more.
This exchange between Zod and Jor-El's digital copy. The deadpan tone of Zod's voice is what sells it.
Jor-El: You're talking about genocide. Zod: Yes. And I'm arguing its merits with a ghost.
That one unfortunate crewmen who fell off from plane let out his Stock Scream.
When Superman and Lois finally kiss...Perry White seems to smirk.
Also, the look Lois gives Clark after their Big Damn Kiss, going, "You know, they say it's all downhill after the first kiss." She is turned on like crazy.
To which Clark responds that he's fairly sure that rule only works with humans. Beat; Lois kisses him again (a la "Oh, Clark, shut up and kiss me...").
The fight with Zod gets into a partially-constructed building at one point. In a "blink and you'll miss it" moment, Zod whacks Superman into a "days without an accident" counter, knocking the numbers off and reverting it to zero.
There's also the way Supes gets knocked into it; Zod comes after him with a huge metal girder, Superman heat-visions it until it's so short, it misses him. He closes his eyes to shut off his heat vision...and Zod promptly whacks him with the shortened girder, making the whole maneuver rather pointless.
Ironically, the Man of Steel was knocked off by a steel.
The Carl's Jr/Hardee's commercial featuring Metropolis City Service dealing with Superman's potholes. Just as the city worker amends that they'll be done "before lunch" to "right after lunch" after seeing a pair of transformers fall (despite the large mess all over the place), Superman lands further down the street, creating yet another pothole.
City worker: (gives a look of "Dude, again?") Superman: (gives a rather sheepish and apologetic look) City worker: (salutes with his burger) All good, man! (turns to camera) Maybe a little overtime.
For Dragon Ball fans, one of Zod's minions being named "Nam-Ek" can be considered funny.
During a guest appearance on The Graham Norton Show alongside Henry Cavill and Amy Adams promoting the movie, Russell Crowe related how one of the infant actors playing baby Kal-El had a "full evacuation" and the... results got on his costume, making it slippery, and he ended up holding the baby close to him. Crowe also mentions that there was "a lot of air involved" with another baby actor.