Deliberate mistake: When Supergirl flies out of the lake upon her arrival to Earth she's wet. When she lands on the shore she's suddenly dry.
Suggested correction: Incorrect. She's not wet when she comes out of the water. She emerges from the water dry in an (incredibly wonky) effects shot. Why she's dry coming out of the water is unclear, but it presumably has something to do with the teleportation process for how she got to Earth considering her costume also suddenly appears on her as well.
Deliberate mistake: For dramatic purposes, when the film ends, Supergirl leaves a cloudy trace while she flies. No trace was seen during her previous flights.