Revealing mistake: In the final confrontation, when the force of shadows pulls Supergirl forward her body begins to tilt backward as she struggles. As she does, you can see the straps of her flying harness begin to peek out from underneath her super skirt. (01:53:40)
Revealing mistake: When Supergirl flies through the window to fight the invisible monster, half of the screen shows her jumping in a school uniform and the other half exiting with the Supergirl outfit. Watch closely and you'll notice that her halves don't match, giving the sense that she is missing part of her body.
Revealing mistake: When the invisible monster crushes Supergirl against a steel door, she flies to fight him and the wires holding her are visible.
Revealing mistake: When Selena breaks the brick wall, the concrete holding it flutters, revealing it's a mere brown piece of fabric.
Revealing mistake: When Supergirl flies out to fight the invisible monster, the shadow of the crane lifting her is reflected on the building.
Revealing mistake: When Supergirl flies towards the mountain and passes by the town close to the pavement, she casts no shadow.
Revealing mistake: In the castle, while Bianca says "I think I'll be going", the glass on the mirror has wrinkles, revealing it's a piece of aluminium foil.
Revealing mistake: After Supergirl lands on Earth, she flies very close to a lake, but she doesn't have a reflection in the water.
Revealing mistake: When Supergirl is passing by the town, flying towards the mountain, she flies very close to the ground but no one looks at her.
Revealing mistake: When Supergirl is flying at super speed, the cars from the green-screen movie are also sped up.
Revealing mistake: When Supergirl is writing her letter of recommendation at super speed, it's way too obvious that the scene has been sped up in several takes because the leaves in the background move fast and in a very weird and unnatural way.
Revealing mistake: When the invisible monsters throws Supergirl against the street light, the place she falls looks uneven with the rest of the lawn, and is filled with chunks of grass to hide the landing mat. In a wider shot all this atrezzo disappears.
Revealing mistake: When Supergirl is flying to Earth, part of her head disappears due to the blue screen used. Also, some sides of the spaceship either disappear or become transparent.
Revealing mistake: When Kara comes out from the lake, the wire cable that pulls her up is visible.
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.
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.
Revealing mistake: During the beach scene, when Supergirl flies in front of Ethan, the wires holding her are visible.
Answer: It's never explained, she could have changed at super speed. In Superman II, when confronted by the super criminals at the Fortress of Solitude, Superman did a disappearing and reappearing act. So did the criminals. It might be a similar thing.