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Adaptation Distillation: Unlike the comics where the bottled city of Kandor is kept by Superman because he could not restore it to full size, the end of the film sees Kandor restored on a new worldnote probably because Metropolis was also bottled and restored in the film and the writers would have otherwise had to explain why one city could be restored and the other one left out.
Conservation of Ninjutsu: One Brainiac probe is a mildly difficult opponent for Superman before he knows what it is. He mows them down in droves after that. Then goes back to having trouble with one again.
Conspicuous CGI: Not as blatant as some instances in the DC animated line, but vehicles such as the helicopters in the opening scene are noticeably CGI.
Does Not Know His Own Strength: Lois lampshades this in regards to Supergirl as she takes out the thieves in the beginning, even using the trope name word for word.
Discussed. Kara explitily states that unlike Clark she did not grow into her powers like he did, she just suddenly had them and unlike her cousin does not have a lifetime of practiced control with them.
Enhance Button: Consciously averted with Perry asking how far an image could be zoomed in before loss of detail.
Eye Scream: Brainiac having his eyes replaced with cybernetic ones in the opening sequence.
Fish out of Water: Supergirl, who showed up on Earth a few months ago well into her teens. For example, she finds the idea of eating pigs off-putting.
Hoist by His Own Petard: Brainiac's decision to spare Krypton because it was going to explode anyway ultimately doomed him. More generally, Superman escapes Kandor by destroying the drones sent to stop him then hitching a ride when they're beamed out for repairs.
Holding Out for a Hero: Perry speculates that attempting to make humans self-sufficient may be the reason Superman has been gone for weeks.
Huge Guy, Tiny Girl: They're both superpowered aliens, and her strength and abilities rival his own, but it would take four or five of Kara to make one Clark.
Maybe Ever After: A mild version of this trope. The last scene before the closing credits shows Clark proposing to Lois in front of the Daily Planet staff. We don't hear her answer but given the conversation they have about their relationship earlier in the movie, "Yes" seems to be a safe assumption.
Men Are the Expendable Gender: No women are seen harmed or killed on screen. We clearly see probes going into Superman's skull complete with blood, but when we see probes about to go into Supergirl's ears, the scene cuts just before it happens.
My Skull Runneth Over: Brainiac hooks Superman up to his archive and starts downloading, betting that Superman's brain would liquify after only one world. Superman then beats Brainiac by taking him out of his ship, overloading him with the constant shifting data of a living world which he so desperately tries to contain in his bottled cities.
Red Eyes, Take Warning: Superman's eyes glow red when he's readying his heat ray vision, or often just when he's really pissed. Brainiac's eyes are always red, but they glow more brightly when he's angry.
Shoot the Hostage: Bizarrely, the police in the opening have zero problem shooting at the thieves while they're using Lois as a hostage. The ringleader actually points this out, figuring they must not be on good terms.
The Stinger: Brainiac's cube boots up in the Fortress of Solitude.
Strong as They Need to Be: The Brainiac probes are strong enough to fistfight Superman, but weak enough to be shoved out a window by Lois Lane.
Super OCD: Brainiac Up to Eleven. Due to what Zor-El believes to be a bug in his programming, he must learn everything in the universe...but since intelligent beings are constantly changing, he destroys their planets and keeps what he does collect artificially stagnant.
Teens Are Monsters: When Supergirl and not Superman comes to rescue Lois at the beginning of the movie, Lois points out that her kidnappers should be very afraid, given their opponent is an entity with all the strength of Superman along with...the hormonal angst of a teenager.
Tempting Fate: Ma Kent points out that Superman probably acts the way he does because he's afraid of history (i.e. the destruction of Krypton) repeating himself. Cue the appearance of an envoy of the guy who stole Kandor...
The Theme Park Version: The fact that Brainiac's bottled cities are this to the cultures they're meant to represent is repeatedly referenced.
Thou Shalt Not Kill: Played with in some of the exchanges between Superman and Supergirl, with the latter strongly implying she's willing to use her powers to kill if necessary. (Later, when we hear of her taking on Somali warlords, it is taken as read that she isn't necessarily letting the bad guys walk away.)
Superman said that he would free them and find new planets for them to live on. He probably did that after defeating Brainiac.
We don't know if Kara is reunited with her Black Best Friend. Or if the other Argoans who joined Zor-El and Alura are still alive.
Wrong Genre Savvy: The thieves in the beginning think they've got their escape all planned out, having timed their heist to coincide with a natural disaster elsewhere in the world so Superman will be occupied. They neglected to read about the second Kryptonian, then Superman shows up anyway.