Audio problem: When Nigel holds Linda back after computing class, Lucy mutters "Oh, shoot", but her mouth is saying "Oh, shit."
Continuity mistake: At campus, Supergirl holds the road map with her left hand on the side of it. A frame later it lays on the middle of it.
Continuity mistake: When the red haired girl is breaking the pipes, the nerd behind hair has a couple bangs of hair on her forehead, or a lot, depending on the angle.
Revealing mistake: When Supergirl is about to fly through the water tank to extinguish the fire, note the patch on the tank where the hole later appears, painted on a darker grey colour.
Revealing mistake: During the bulldozer scene, the truck loaded with hay skids on the road. Skid marks from previous takes are visible, and their colour also changes intensity.
Continuity mistake: When Supergirl runs inside the diner to change into her super outfit, the two girls next to the bathroom door disappear between shots.
Revealing mistake: Right after Supergirl saves Lucy in the bulldozer and dismounts its front part, when she is about to land in the yard to save Ethan, wires holding her are visible.
Revealing mistake: After the bulldozer destroys the gas station, two cars crash against each other. Their hoods are already damaged before the crash.
Continuity mistake: When the bulldozer destroys the gas station's roof, a column falls on top of a green car. Its position changes between shots.
Continuity mistake: When the bulldozer is about to destroy the gas station, two workers next to a green car run away. In the close-up, several seconds later, they're back next to the car, repeating all previous movements.
Continuity mistake: When the bulldozer destroys the bar, wooden planks on top of the door suddenly appear between shots, and the ones to the left of the door disappear. Also, the man on the far left's arms swap from straight to bent between shots.
Continuity mistake: When the crazy bulldozer is about to trap Ethan, check the left side of the street: A woman in yellow stands next to a man with a red jersey, who disappears when the angle changes.
Continuity mistake: Right before the final fight, when Selena is about to say "Power of shadow", smoke comes out behind her. In a wide angle the smoke is gone and it's appearing on the left side first, and later on behind her back.
Revealing mistake: During the beach scene, when Supergirl flies in front of Ethan, the wires holding her are visible.
Revealing mistake: When Kara picks up the Omegahedron, you can briefly see a ring underneath, around her fingers, to make it turn around.
Continuity mistake: Selena says "Bad luck" and places her hand on the fridge door. In the next shot, only the tips of her fingers are on it.
Revealing mistake: When Supergirl falls on the planet ground and gets released from the mirror trap, she gets up and the hard floor stretches down, revealing it's a rubber mat to soften her fall.
Continuity mistake: While Selena is burning the chicken, in the close up shot big flames come out, but a split second later, from a different angle, there's just smoke.
Continuity mistake: At Selena's picnic, the label of the champagne keeps turning to face the camera.
Continuity mistake: When at home, Selena says that the world is at her wish and looks down at the bronze sculpture which she is holding close to her chin. In the following angle her hand swaps to stomach level.
Answer: The Omegaahedron is the power source for the whole city. It supplies the air, the dome that protects them, the lights, and the machines they need to survive.