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.
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.
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.
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.
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.
Continuity mistake: Supergirl's bracelet swaps wrists while she's flying at night.
Continuity mistake: When Selena is holding the glass champagne and says "I can't wait 'till the world is mine", from a back shot her finger is below liquid level, in the following shot it is above it.
Continuity mistake: When Supergirl heats the monkey wrench, it swaps positions between shots.
Continuity mistake: The hole that Supergirl makes in the water tank changes shape between the close and wide shots.
Continuity mistake: In the girls' dorm, when Supergirl is trying the bra on, the teddy bear in the back changes position between shots.
Continuity mistake: Supergirl crushes a rock and gets dirt all over the sleeve of her suit. A second later dirt is gone and the suit is clean.
Continuity mistake: Selena starts to say that everything is history and turns around to say the world is hers. Right then, angle changes and cupboards appear on the right from nowhere. When the angle changes, the cupboards disappear.
Continuity mistake: When Supergirl enters her dorm, the Cornflakes box changes position from standing upright to sideways.
Continuity mistake: After her fight with the invisible monster, Supergirl walks by the broken steel door she fell against, and it looks more crumpled and worn out than before.
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.
The question was why would Zoltar need permission to use the Omegahedron, not what it could do.