When the Siren arrives in Commissioner Gordon's office, she is wearing sandals and her hair is tied back. However, when she escorts the commissioner to the police garage to sneak into the Batmobile's trunk she is wearing boots and her hair is loose.
Robin brags that his bat-earplugs will protect him from the Siren's song, since they screen out any sound above 14,000 decibels. However, decibels measure the volume of sound (how loud or soft a sound is), while the Siren's power depends on the frequency of the sound.
Siren claims that singing the "antidote note" - three octaves above high C - would destroy her voice. However, the Siren is described as having a seven-octave range, with an upper range that only dogs can hear. Assuming her lowest note is at middle C (two octaves below high C, and about the average soprano's lower limit), the antidote note is only five octaves higher, and should be well within her ability without any damage to her voice.
The Siren's plan to steal the Wayne fortune ends with Bruce Wayne leaping to his death immediately after signing over his fortune. However, legal documents require the signer to be of sound mind in order to be valid - if Bruce had jumped, it would have been prima facie evidence that he was not of sound mind.
The Siren claims the note she uses to put men under her spell is two octaves above High C. However, the note that was actually used was F Sharp (F#). Therefore, this makes Siren's note two octaves above High F#, not High C.