Continuity mistake: When Ethan falls unconscious on the couch, his arm is close to his face. In the following shot it has moved down.
Continuity mistake: When Ethan enters Selena's house, Selena opens the fridge. Her position behind the door changes from being in the middle to the right of it between shots.
Continuity mistake: When Supergirl visits the principal's office, he is holding the glass down, close to the medicine bottle. When the angle changes, the glass is up without him having raised it.
Continuity mistake: When Supergirl wakes up in the woods, the baseball's stitches face different sides depending on the angle.
Continuity mistake: Selena's friend places the bottle of milk on the center of the burning chicken to extinguish it. When the angle changes the bottle is on the left side of the chicken.
Continuity mistake: Inside the girl's bathroom, when the red haired girl comes running in with her friend, watch the towel in the back: In one shot it's laying messy on the sink, and a second later it's neatly folded.
Continuity mistake: Supergirl arrives on earth, lands in a forest in broad daylight, walks four steps and when she stares at a lake it's suddenly dusk light.
Continuity mistake: While Supergirl is flying around the city her bracelet is on her right hand then on her left.
Continuity mistake: Before Kara used the sphere to travel to earth she did not have the blue/red suit with the cape but suddenly the suit comes out from nowhere.
Continuity mistake: While Supergirl is talking with Zalter in Kripton beside them there are a couple with a man and a girl who disappear between shots and then reappear again.
Continuity mistake: When Jimmy brings the onion rings, the guy on the left swaps between having his arms down to crossed, between shots. (00:54:32)
Continuity mistake: When Supergirl flies over the field with the horses galloping below, the horses disappear in a couple of wide shots of her.
Continuity mistake: When Selena toys with the Omegahedron and it goes berzerk, she and Bianca hug. The position of her arms isn't continuous in any of the shots.
Continuity mistake: When Selena's car arrives at the campus she is not in the car. A shot later she appears inside.
Continuity mistake: Inside Selena's car, the first shot of the Omegahedron shows her thighs and the book on her lap. In the following shot Selena and the book vanish.
Continuity mistake: When Selena plays with her Tarot cards, the one on the far left corner has a round square drawing on the base. In the close-up it's a different card.
Continuity mistake: After the hockey ball crashes against Supergirl's back, a girl with glasses staring at her is holding her hockey club. A shot later her arm is raised.
Continuity mistake: When the school bus arrives at the campus there are only 3 or 4 girls inside. From the shots inside Selena's car at least 9 girls leave the bus.
Continuity mistake: When Supergirl is kicking the truck guys' asses, the big one has long hair, but in the angle from behind, right before she kicks him, his hair is short. (00:24:35)
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.
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.