Superman's origins on Krypton, being found as a baby and raised by Jonathan and Martha Kent, discovering his powers, resolving to use his powers for good, and creating the costumed Superman persona with his parents' help as a way of keeping his heroing and the resultant celebrity separate from his personal life as Clark Kent.
Told from Lois Lane's point of view as she attempts to get the first interview with Metropolis' new superhero (and gets a bad first impression of new colleague Clark Kent).
Superman investigates a vigilante in Gotham City, and winds up helping Batman crack his latest case. The two heroes gain a grudging respect for each other, but (in deliberate contrast to the Pre Crisis status quo) are too different in outlook to become close friends.
Superman and Lex Luthor meet for the first time, when terrorists attack one of Luthor's parties. After Superman cleans up the terrorists, Luthor reveals that he knew they were coming but had his security hold back so he could see Superman in action, and offers Superman a job. Superman's response is to run him in for endangering his party guests.
An attempt by one of Luthor's pet scientists to create a Superman duplicate results in a bizarre warped copy that attempts to live Superman's life, trying to do good deeds for people who are as afraid of it as of what it's trying to rescue them from, and forming a connection with Lois' sister Lucy.
Clark Kent goes to visit his parents in Smallville, reminisces about the past, and discovers a recording of Jor-El that teaches him about his Kryptonian origins. He affirms that, although he appreciates knowing where he came from, he now thinks of himself not just as an alien visitor but as a citizen of Earth.
Batman Gambit: Batman has one ready to keep Superman from immediately apprehending him for vigilantism before having a chance to see the good he does. It's brilliant, it's specifically tailored to Superman's strengths and weaknesses, and (especially the key detail revealed at the end of the issue) it says a lot about how Batman sees the world; Batman's Exact Words are that if Superman touches him, it will set off a bomb hidden "somewhere in Gotham City", which will kill "an innocent person."
Batman: It's a touch Machiavellian, I admit. But my end justifies my means.
On the last page, Batman reveals that the bomb was in his utility belt the entire time. The only life at risk was his own.
Foreshadowing: In the first issue, the Kents are being spied on. It was Dr. Emmett Vale, who used his science to create Metallo. The same character is the one snapping a pic of Supes without him realizing at the end of issue #4.note Superman states in internal monologue that he tries to make himself blurry and indistinct for photos and video, to prevent people from taking an exact measurement of his height, what he looks like, and so on.
Groin Attack: In Issue #4, Lois and Clark encounter a couple of South American terrorists onboard Lex's luxury liner during a party and even though the terrorists themselves are armed, Lois isn't afraid of them as she kicks one of them in the groin so that she can then get his gun and start to fight back against the terrorists until Superman arrives.
Clark's secret identity would be his "Fortress of Solitude". It would be some time before the actual Fortress of Solitude was re-established Post-Crisis, and at first it was just called "the Fortress".
The plot of Issue 5 is similar to Bizarro's debut in Superboy #68.
While the cover of each issue features a character facing the reader, Issue 5 has Bizarro facing his back on the reader. A nod to his pre-Crisis counterpart being a mixed-up, backwards creature.
In the issues where he appears, Lex Luthor sports a head of red hair, but it is clear from the progression of time that he is losing his hair (Lois at one point says, "You look like Fred Mertz!"). In a Silver AgeSuperboy story, Lex blamed Superboy for an accident that resulted in his being bald. In this story, he blames Superman for his being arrested like a common criminal. It's not said, but it's implied that Lex blames Superman for his stress-induced male pattern baldness as well.
Political Correctness Gone Mad: In this series, Kryptonians were born in a "birthing matrix," and immediately isolated from every other Kryptonian. In this manner, there was no way anything one Kryptonian said or did could possibly offend another. When Jor-El contemplated sending his child to Earth, he initiated a face-to-face meeting with the child's mother, Lara; the first such meeting between Kryptonians in several hundred years. When Lara views Jor-El's images of Earth, she is horrified at the sight of a field worker with his shirt off. Nevertheless, Jor-El convinces her to send the birthing matrix to Earth and they continue their illicit affair until Krypton is destroyed.
Byrne borrowed elements from the 1978 Superman film. Krypton was depicted as a cold and emotionally sterile planet, and Smallville was placed in Kansas. He also kept Ma Kent alive to see Superman debut, though he kept Pa alive too (Pre-Crisis, both had died when Clark was still Superboy). Clark also never became Superboy like in the film.
Byrne's characterization of Clark was derived from George Reeves's portrayal in The Adventures of Superman TV series. Unlike Christopher Reeve's Clark which was an act once he got the Superman costume, George Reeves's Clark reflected Superman's true character more, being much less timid and wimpy. For Byrne, Clark was as much or even more of "the real person" as Superman was. This is basically how Clark has been portrayed in the TV shows (Lois and Clark, Smallville, the DCAU, etc.), but the films (Superman Returns, Man of Steel) have ultimately stayed with the idea of Kal-El, and his parents from that side, being more important than Clark Kent and the equivalent parental figures. (Superman Returns is a given, but Man of Steel? Well, in the DCAU, the costume was stitched by Ma Kent. In Man of Steel, it's Kryptonian battle armour given after a Jor-El heroic purpose lecture. Draw your own conclusions.)
Secret Keeper: Lana Lang, instead of Pete Ross, in this continuity.
In issue #3, the Magpie kills one of her henchmen using a re-enactment of the "Happy Birthday" gag from the Looney Tunes cartoon "It's Hummer Time!" (it's a Non Fatal Explosion in the cartoon, but the henchman doesn't have the good fortune of being a cartoon character. Plus she puts the dynamite right in his mouth).
Lois insults Lex by saying he's starting to look a lot like Fred Mertz.
Steven Ulysses Perhero: The villain Batman is after in issue #3 is the Magpie, who is driven by a compulsion to steal and hoard valuable artworks. Her real name is Margaret Pye.
Superman Stays Out of Gotham: Addressed in the third issue. Batman tells Supes that "Defending a planet and cleaning up a city are two very different things... Gotham City isn't your turf. It requires a different approach." By the end of the issue, Superman warns Batman he'll come after him if he ever cross the line.