Strictly speaking, the pressure of an alligator's jaws is such that a man keeping one's mouth from closing is quite impossible, or, at the very least, attempting to do so is unwise. It is far easier to keep an alligator's mouth closed and tie it shut.
The Sewer King's line "A few hours in the light will make Jack a bright boy" echoes the proverb "All work and no play makes Jack a dull boy".
This is the first episode of the series to show Batman's soft spot for children, displayed when he expresses a desire to kill the Sewer King for his abusive treatment of them.
There is a reference to classic composer Johannes Brahms. Alfred listens some of the Brahm's music while Bruce talks about leprechauns.