Other mistake: When she breaks the TV's with her "voice" they pan to the salesmen. The glass display case is intact. Had her pitch actually been able to break glass the display case would have gone as well.
Continuity mistake: When Madison runs from the ice-skating she is barefoot. In the next shots she magically has managed to bring her shoes and has put them on.
Suggested correction: Right before Madison rushes away from the ice rink (01:10:10), she grabs her ballerina flats, and when she runs away from Allen, she's barefoot while holding the flats in her left hand. Then, the skate rental guy tackles Allen. When it cuts to Madison in the shot facing her back, she's still running barefoot while holding the flats in her right hand.
Continuity mistake: Before Allen jumps to chase the mermaid, the helicopter is above him and he looks up. His hair doesn't move despite the rotors above. Then in the following shots it finally does move.
Continuity mistake: When the army exits the lab to find the mermaid the pavement is wet and the sky is cloudy. The following aerial shot shows the pavement dry and the light sunny. The light keeps changing with no continuity throughout the scene: cloudy, sunny, dawn, dusk.
Plot hole: Why would Madison take a bath in steaming hot water? The ocean water is warm or cold depending on the area of the ocean. So, it makes no sense as to why she does this.