After her first sparring session with Alex, Kara is stiff and sore, brushing it off as taking a kickboxing class. But Kryptonians have a solar-powered Healing Factor, something which is consistently referenced, so any aches and pains should have vanished almost immediately, even with Alex using Kryptonite emitters to suspend Kara's powers. But, Kryptonite! Kara isn't sore from the workout or beating, she's sore from lingering Kryptonite poisoning.
The buildup and reveal that Hank Henshaw is really J'onn J'onzz, the Martian Manhunter and not Cyborg-Superman was well done by the writers because even as it was made clear that Henshaw wasn't a normal human and people guessed he could be one of the two, the hints that were dropped could have gone either way.
The superstrength and glowing red eyes could have applied to either.
Both characters had experienced the tragic loss of loved ones.
When he knew Alex was working behind his back—indicated by his eyes glowing red—it could have been due to J'onn's telepathic abilities or that she was doing it on a computer, which a cyborg could be in contact with and monitoring.
Henshaw helping people and performing good acts could have been either Martian Manhunter's true heroism or Cyborg-Superman's original Villain with Good Publicity ploy.
The story Alex is told of how her father died plays in with the Martian Manhunter's comic backstory: the DEO tracked him down in Peru, and canonically J'onn J'onzz is considered, by the people in the southern continents, to be a hero on par with if not surpassing Superman in fame.
Henshaw explicitly stated that the DEO was not supposed to deal with human threats when Alex assisted Kara with Reactron using DEO resources and seemed reluctant to help her, but then had DEO assets deployed to deal with bombings that were clearly human in origin and when Livewire appeared he was openly assisting Kara in dealing with her. The apparent sudden turn around from reluctant to enthusiastic assistance makes sense given The Reveal that he's the Martian Manhunter. Thanks to Kara he's been given the excuse and opportunity to finally be able to be the superhero the character is.
Cat chewing out Leslie for attacking Supergirl might seem hypocritical since she wrote an equally harsh article about Supergirl. However, Cat only criticizes Supergirl's actions. Leslie, on the other hand, mocks Supergirl's appearance, personality, sexual orientation, and genitalia. To Cat, criticism of someone's actions is okay, no matter how harsh, but personal attacks are not tolerable. Also, Cat is trying (in her own, backhanded way) to help Supergirl improve, pushing her through legitimate criticism to do and be better (something Cat all but outright states in that very episode). Leslie's just being a bully.
In Episode 2, when Astra tells Hank he can't hurt her, he replies "You are so wrong," before stabbing her with a Kryptonite dagger. With The Reveal in Human For A Day, it's clear he wasn't just referring to the dagger: as a Martian, Henshaw is one of the few living beings that can effectively fight a Kryptonian.
Initially, Henshaw explained the DEO was set up in response to the existence of Superman, and he didn't get along very well with the organization. Yet, oddly enough, assuming Kara told Clark at some point who she was working with, he didn't try to intervene or convince her not to. "Human for a Day" and "Hostile Takeover" makes it clear why: he knows who really is in charge of the DEO and that he's an ally, not an enemy.
Jimmy initially reassured Kara that Cat would never recognize her as Supergirl because she wouldn't look at Kara and see a hero. And she didn't... until Kara actually helped her out of a jam in "Hostile Takeover" and made Cat think twice about her. Then Cat put it together immediately.
Henshaw reveals to Alex that the only person other than her that knows his real identity as a Martian is Superman. Didn't he promise Alex's father that he'll protect her and Kara, and does so by doing a Dead Person Impersonation of Shaw? So that means Mr. Danvers knew, right? Now who plays Mr. Danvers again? That's right.
You might be wondering what J'onn is doing hiding amidst an organization specifically meant to hunt and apprehend alien interlopers... until you remember he's still staying true to his comic book name: He's hunting dangerous criminals in manhunts.
When Barry is trying to figure out what happened, he lists several Arrowverse heroes, but ends with Zoom. He wasn't just listing names. As soon as it became clear he wasn't on Earth 1, he listed the one person they both would have heard of on Earth 2. Kara not recognizing anyone means a new Earth. This is also why he mentions Firestorm. Jax and Stein work in Pittsburgh, and may be more well known elsewhere. Compared to someone like Black Canary, who would only be known in Star City.
Kara's constant tendency to stumble over her words makes a little more sense when one considers that English is her second language.
Supergirl defeating Reactron when Superman couldn't can come off as an Ass Pull, but Superman appears to operate self-reliantly, and though smart, doesn't know everything. Kara has her friends and the DEO to give advice, do research, and come up with alternate strategies. A Show, Don't Tell example of The Power of Friendship.
Cat does not like millennials and was actually reluctant to hire Kara because she is one. Except she actually got her wish, as Kara is actually not. Kara was stuck in the Phantom Zone for twenty four years, and because of that she did not physically age. She was actually born on 1966, technically making her a part of Generation X.
Metallo having such a glaring weakness (the exposed kryptonite on his chest) is justified since his body is Made of Indestructium, so it would must surely block most of the radiation, if not all of it, if the kryptonite was inside his body, therefore losing his main edge against a kryptonian opponent.
While it seems strange to send a pre-teen off by herself, it makes more sense when Kara mentions "changing [Kal's] diapers when they were on Krypton". She probably babysat him most of his life on Krypton and was still small enough to fit in the escape pod, yet old enough to take care of him when they arrived on Earth.
Regarding the Episode "Welcome To Earth", there's another level of racism that was foreshadowed but not explicitly dealt with in the episode. The show has already introduced Green Martians like J'onn and White Martians. Care to take a wild guess at which kind M'gann M'orzz really is?
If Madame President is really an alien, Scorcher wasn't trying to kill her. She was trying to expose her.
Roulette was released within hours of being arrested, because someone ordered her release. She clearly has a lot of pull with the city's upper class, none of whom would presumably testify against her, and even a lot of the aliens (apparently) signed up willingly and were loyal to her. Any investigation into the fights themselves would be stonewalled, or Roulette has plausible deniability; the only thing the city could do was charge her with operating without a liquor license and hope to go from there. If the head of the DEO had turned up dead at her event that would have been a whole other story, but he wasn't killed. In a way, rescuing J'onn might have been the reason Roulette didn't stay locked up.
Draaga, despite being strong and tough enough to fight a kryptonian, backs off when threatened by a normal handgun. It's understandable once we remember that he has a bad knee from a previous fight, meaning that he is neither Nigh Invulnerable nor has a Healing Factor, so he'd be wary about being shot, specially with weapons he has never faced before, being an alien and not familiar with Earth weaponry or if his own species can resist it.
The Cadmus Lead Scientist told Lena that Chet and his cronies were going to hit her party. She knew Lena would beat them at their own game, and give her a way to kill them after they were arrested remotely.
Kara's getting wasted on one drink isn't just because it was a strong drink. She's never been drunk before. Like a lot of new drinkers, she has no idea how to handle being drunk and no tolerance for alcohol. It makes total sense that she would be flailing all over the place.
Mon-El understanding Kara's forehead crinkling is her lying, meaning he was paying attention to her and falling for her.
The fact that when girls were buying them drinks, they weren't just sending them to Mon-El, but to Kara, as well. Humans would assume that if he was drinking with her, then they're taken, or would at least only send over a drink to the individual they're interested in. This could be revealing that a lot of the aliens in the bar still aren't quite familiar with the aspect of Earth culture or, if they do have drink-flirting on their home planets, that they are quite liberal with sexuality and monogamy...
Mon-El was scared of being on Maldoria, but not because he was afraid of getting killed or even captured. He was scared of being recognized. As royalty, the slavers would remember him as a buyer, and do exactly what the Dominator did: bow and scrape, treating him like royalty. In fact, the reason he acts buffoonish, enjoying low-class entertainment is that he was never permitted to on Daxam, and if Kara and the others find out he's royalty, he's afraid he won't be able to enjoy slumming it anymore, or being treated as a (relatively) normal person.
Why is M'gann in human form in the mental bond she forms with J'onn? Sure, it's probably to save on budget in real life, but it could also be because she feels far more comfortable (and doesn't hate herself) as Megan the human than as a White Martian. An interesting variation of A Form You Are Comfortable With. It's also more neutral. Appearing as a Green Martian, who she would rather be (and what she chooses later to fight as), could be seen by J'onn as offensive.
Absolute fridge brilliance is the setting up of Kara and Lena as seeming diametrically opposite incarnations of the same person (completely separate to the "Super VS Luther" opposite that is being played): they are both adopted and left only with a sibling and a mother, but Kara was raised by warm alien-loving people and Lena by cold alien-hating people. But they both have one very important thing in common, and that is an intense and close relationship with their adopted sibling (so what if Lex is evil, he was really good to Lena) — and this is why the name of Kara's Canon Foreigner sister is so important. Alexandra Danvers. Alexander Luther. Their siblings are reflectively the same, and having such strong bonds with them is perhaps what makes them well-rounded fulfilled people. This goes further: Alex, with her father taken away from her as a direct result of the presence of an alien in her life, could have easily gone the same way as Lex, but she has the relationship with her mother that Lex didn't. Now, with Lex incarcerated, Lena seems to be relying on Kara for this kind of bond.
Lena changing the name of Luther Corp to L-Corp. It's not her initial, it's somebody else's surname (El, the family of Superman and Supergirl), foreshadowing that she's on the side of the Supers. Also, "L" sounds like "elle" (her).
The way the various characters react to Jeremiah's "rescue" from Cadmus is entirely consistent given their relationships with him and their own histories:
Mon-el, not knowing him at all and only recently meeting Kara's family, is the only one looking at the situation objectively because he has no emotional involvement.
Winn, as a close family friend of the sisters, initially sides with them but he doesn't personally know Jeremiah either, so it doesn't take much to convince him to at least look at the situation.
Kara, as the adopted daughter, is very close to him but still eventually willing to listen to evidence against him when forced to, both because she was old enough to know he wasn't always her father, but also because she's had both her real parents revealed to not be the upstanding paragons she thought they were, so she can accept the possibility parents aren't perfect.
Alex lost him when she was a teenager and so is the most unwilling to see him as anything other than the daddy she's missed and remembers, and as the man she was told heroically sacrificed himself.
Eliza, as an adult and wife of many years when he disappeared and was presumed dead, had over a decade and the emotional maturity to deal with the loss before she found out he was alive. As the one who knew him best, she's also aware that things have changed because she has changed so she can't expect him to be the same either.
The relationship to their parents also plays a role. Kara knows parents sometimes aren't what you think they are. Winn's father is a supervillain and mass murderer, and based on what Mon-El has said, his was no prize either. Both of them wouldn't be the kind of people to overlook another's possible problems just because that person was a father.
In "Mr. and Mrs. Mxyzptlk", Mxy had himself in the role Aaron Burr and Mon-El in the role of Hamilton during their duel. Considering the play Hamilton, Mxy's behavior in the episode, and Mon-El's overall storyline, it all makes perfect sense.
Kara finally learned that Mon-El is the Prince of Daxam. She gets angry, but it's not until he recounts the story of how he really escaped Daxam's demise that she reaches her Rage Breaking Point. Why? Because in that tale, his bodyguard kills people to save him, the last being a Kryptonian whose pod Mon-El ends up using. Basically, she and Mon-El only met because one of her own people was killed. What was arguably the worst day of her life and for others turned out to be a lucky break for Mon-El-who barely even seems to see this as wrong. Ergo, Kara means it when she states that Mon-El was a big part of a culture that benefited from the plight of others. To her, he now embodies everything wrong with the Daxam way of life, and therefore everything that she is against morally. He is an example of everything she is against as a person, and is offensive to her principles. Rhea has no idea how right she is when she states that Kara comes from a people who are unforgiving and that she sees Mon-El as not good enough for her. Thanks to recent events, he may never be.
There's a quick bit in "Ace Reporter" when Kara is trying to bake and hauls a pan out of the oven. She isn't wearing any hand protection but then the realization kicks in...she's Supergirl, of course she could take something straight out of the oven.
No wonder Cat figured out who Guardian is right away. Not only can she see James' eyes through the mask, but he had weights in his office, was mysteriously absent from reporting because he's supposedly a coward...honestly, it's not that difficult. Which of course foreshadows the fact that Cat also knows that Kara is Supergirl.
In "How Does She Do It?" Supergirl accuses Hank of sending drones to spy on her, he replied "If I wanted to spy on you you'd never know" Invisibility is one of Martian Manhunter's powers.
James being a black belt may seem like an Ass Pull, but it actually might make sense: He's best friends with a superhero, and so probably got kidnapped by bad guys, especially since Lex presumably knows Superman's real name. After that, James most likely decided to learn how to protect himself. In addition, James becoming the Guardian may actually make sense of a lot of the Adaptational Attractiveness. James' Hunk appearance may be because he started bulking up and training with the idea he might become a superhero on his own, or because of the above idea.
The Reveal in the season 2 finale that Rhea's blood is heavily laced with kryptonite actually makes her behavior throughout the series make a lot more sense. Ever since the Bronze Age, we've known that kryptonite does have negative effects on races other than Kryptonians, and some fans have even theorized that overexposure to the stuff may be why Lex Luthor is so prone to insane behavior. So, if Rhea is so saturated with the stuff that she bleeds green, then it's probably not done her sanity any good at all.
In season three, Kara lashes out at Mon-El over their relationship while under the influence of a psychic attack. However, pay attention to what she complains about, for she may be really angry with herself: she lists all of the things he did before they ever got together, and then states that she gave her heart to a "lying jackass". Basically, she is saying that all of the warning signs of him not being boyfriend material were there in front of her face, but she still dated him anyway, only to get hurt in the end. Also, this is happening while he is training her, so once again, she is putting herself in a position to be vulnerable with a guy that has caused her pain before, and she is not happy about it.
At first, when Winn geeked out over Clark Kent being Superman, it feels a bit odd that Winn knew who "Clark" was right off the bat. But given the later revelation that Cat has a total crush on Clark, and that she herself used to work for Perry White, it's entirely possible that Winn has actually met Clark before in the latter's civilian identity.
Even discounting being a puppet for Lex, Vice-President Baker turning out to be a terrible leader and a bigot makes sense when you consider how presidential candidates choose their running mates. It's been centuries since VPs were chosen based on whether or not they'd be a good replacement; instead, they are chosen for complementing the president as best as possible to appeal to parts of the country that the candidate is having trouble with. Older candidates choose younger running mates, liberal candidates choose more conservative running mates.
Watching Winn bond with Carter gets a little disturbing if you know that in the comics Winn's father, the Toyman, murdered Cat's other son Adam. Fortunately unlikely for any of this to play out in the show, since in this version Winn, being the Toyman's son Winslow Schott Jr., acknowledges that his father is a supervillain who deserves to be in prison.
When Hank is angsting over mindwiping the security guard, he says the world is better off without the Martian Manhunter. Makes you wonder what he did to get that name.
The fact that there could be thousands possibly millions of White Martians coming is Nightmare Fuel enough. And in any other world with Superman, it would be terrifying, but manageable. But in this world, there are all of three superheroes, and it took two of them to stop one White Martian.
In Season 2, Mon-El says that he saw Draaga fight on Warworld once. If Warworld exists, Mongul exists and who knows how much destruction he's wrought in this universe.
The No Endor Holocaust aversion with Krypton's destruction. Who's to say that Daxam was the only populated planet ruined by it's collapse?
The reveal that J'onn being exposed to White Martian blood is turning him into one suddenly casts new light on the implications of what the White Martians are. If Green Martians are turned into White Martians via blood transfusion, and the first indication is apparent mental illness, White Martians might in fact just be Green Martians suffering from a horrifying mental illness caused by blood poisoning. If that's the case, it certainly casts new light on their apparent Always Chaotic Evil nature. If that's the case, then it gets worse. If White Martians are just Green Martians with a horrible disease, how did an entire race of them end up underground? At best, an isolated group of Martians developed the disease and ended up isolated from the rest of society. At worst, they were all driven out of society in a sort of leper colony, and only returned when Green Martians had forgotten. On the other hand, M'gann reveals that not only aren't White Martians Always Chaotic Evil, her confidence that there are other White Martians who think like she does or would be at least sympathetic, and she goes back to Mars to start organizing them suggests their situation might be more complicated. Not that this eliminates the above-suggested possibility of how they originated.
As revealed in the Invasion! crossover, the Dominator alien race attacked Krypton. It's very likely that the Medusa virus was created by Zor-El because of that attack.
Mon-El's flashback in "Star-Crossed" showed his bodyguard killing a Kryptonian emissary to give him his escape pod. That emissary was wearing a small but noticeable Superman symbol. Remember back in the pilot Kara explains it was the symbol for the "House of El": Mon-El just stood there while his bodyguard killed a member of her family in cold blood. Which just adds to the Fridge Brilliance noted above regarding her unwillingness to trust him.