In his first appearance, he explains that he was abroad in the Far East. As he finished that statement, a pair of attractive women walk in the room, prompting Penguin to remark with, "Speaking of abroad..."
Later in that same episode, he is heard offscreen smacking some female party attender's butt and is immediately slapped by her for it.
Penguin:(grins) Hmm. Feisty...
In The Batman vs. Dracula movie, when Dracula takes notice of Vicky Vale, a local news reporter, the Penguin confirms that she is attractive by commenting that she had "nice jugulars".
Batgirl got a pretty good line in the episode "Two of a Kind":
Robin: The neighbors say that [Harley Quinn] went freely with the Joker. Wonder what he could want with her? Batman: He saw a vulnerable person he could manipulate, someone good for a few laughs until he got bored. Batgirl: And join us again next week when Batman analyzes the Freudian implications of Penguin's umbrella.
Joker's use of the expression "snafu", unless there's a kid-friendly version of that acronym I haven't heard of...
There is, actually. Situation Normal All Fouled Up.
"Oh, look who's arrived at my coming out party!"
Crossed with Have a Gay Old Time - in the Victorian and Edwardian eras, a young lady's first big party was referred to as her "coming-out" party.