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: When Jimmy brings the onion rings, the guy on the left swaps between having his arms down to crossed, between shots. (00:54:32)
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 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.
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.
Continuity mistake: When Supergirl crushes the rock, her hair is curly and messy. In the following shot it's brushed and straight.
Visible crew/equipment: When Selena visits the school, there's a tube reflected on her window. When her car starts to move we see it's part of an umbrella-like structure used for lighting.
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.
Continuity mistake: When Selena holds on to the fridge door an American flag appears and disappears between shots.
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.
Continuity mistake: After the red haired girl and her friend let go off the monkey wrench, they start jumping and end up close to a steel tank. In the following angle they've moved six feet back.
Continuity mistake: When Supergirl wakes up and sees her bracelet on the floor, in the first shot it is further away from the join between two floor tiles than it is in the second shot.
Continuity mistake: Supergirl lands the colliding car in a shadowy place but a couple seconds later the shadow is completely gone.
Continuity mistake: The mirror in the castle changes to transparent glass when Supergirl flies through it. After the vortex swallows Selena and Bianca, it turns back into a mirror.
Continuity mistake: After the window gets fixed, the position of the cushions around the window differs between shots.
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.
Continuity mistake: Selena parks her car close to the entrance, but in the next shot the car has moved 12 feet to the right.
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.