Plot hole: Superman (or Kal-El) was a baby when his parents sent him away from Krypton before its destruction, and as Jor-El told his son in his first message he would have already been dead by then for thousands of Superman's years. Kara never existed during any of this yet so somehow she instantly recognizes him from the poster on the wall, even though she should have no idea who he is.
Supergirl (1984)
2 plot holes
Directed by: Jeannot Szwarc
Starring: Faye Dunaway, Peter O'Toole, Mia Farrow, Hart Bochner, Helen Slater
Continuity mistake: At the beginning of the movie, Selena drives her car to the right side of the house. When the shot changes, the car is several feet further back and is now heading across the front of the entrance.
Lucy Lane: All you need is a couple of streaks and your ears pierced. I could do it for you, it's easy. You just get a needle, heat it up, dab it with some alcohol, and zap! The guys go crazy.
Linda Lee: My ears what?
Lucy Lane: Pierced. Like and you know, I take a needle, and then I heat it up, dab it with some alcohol and, zap, all the guys go crazy.
Linda Lee: Because I have holes in my ears?
Lucy Lane: What, are you putting me on? Sometimes I can't figure you out, Linda.
Trivia: Helen Slater later played Kara's aunt Lara, the biological mother of her cousin Clark, in Smallville, and Kara's adoptive mother Eliza in the CW's Supergirl.
More questions & answers from Supergirl
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.