The Penguin's Umbrellas
Machine gun
Helicopter
Knife
The Penguin proposes to Catwoman
The Penguin in Arctic temperatures
In Batman Returns the Penguin lives in Arctic World in the Gotham Zoo where it is kept in a refrigerated temperature thanks to a giant fan which is suitable for his penguin pets and himself. His other base above his Mayoral campaign headquarters is also kept chilled with fans, as even Catwoman comments it's chilly in there when she meets with him to form an alliance. Also his campaign van where he has the Batmobile kids ride where he controls the real Batmobile has fans in it to keep the temperature cool. Considering the movie is set in winter in December cold enough for heavy snow, it is clear the Penguin prefers colder temperatures.
The Penguin killing children
Always a point of conflict over the Penguin's persona in Batman Returns that he has never shown any interest in killing children. This happens to be untrue. There was one instance in Detective Comics Annual #1 in 1989, where The Penguin got his hands on a deadly formula which would kill all women and little children in Gotham. Although the Penguin was using it as a method of extortion on Gotham, he was personally delighted at the idea of getting to kill women and children.
In 2011, a mini series called Penguin Pain and Prejudice had the Penguin formulate a scheme where he tried to kill the children of Gotham City by launching robotic rocket penguins into Gotham which released killer attack birds trained to kill children. Although this came after Batman Returns, it was a trait they decided to revisit.
Catwoman anti hero
Catwoman has often been portrayed in an anti hero way, where she will do an act of good, such as preventing a crime. Her motives for doing it have often varied. Everything from personal gratification to personal gain. In Batman Returns this angle was also shown when she saved a woman from a mugger. An act she has also done in the comics.
Selina's cat filled apartment
Selina Kyle has lived in a low rent looking small apartment with numerous stray cats she took in as pets.
Batman and Catwoman fight
Batman and Catwoman have often been portrayed as being physically matched for each other in a fight. Catwoman employing tactics such as her whip, her claws, punches and kicks to combat Batman's physical battle prowess.
The Penguin frames Batman
In The Penguin's very first appearance in Detective Comics #58 he framed Batman for crimes he did not commit. This was also done in Batman Returns The Penguin framed Batman for very serious crimes, and turned the Police and Gotham's citizens against Batman.
Batman and Catwoman unmask to each other
At the end of Batman Returns Batman tried to get through to Catwoman by removing his mask and letting her see the face of the man she cared about underneath. A similar situation was done in the comics, only it was Catwoman who took the first step and unmasked to Batman. But the theme of both scenes is the same. They remove their masks to emotionally connect to each other.
The Penguin eating raw fish
Although The Penguin does eat his raw fish in a more refined manner in the comics in comparison to the movie, he does nevertheless love eating raw fish, just like The Penguin in Batman Returns did.
The Penguin pretends to go straight
The Penguin has a history in the comic books of pretending to go straight, and fooling people into thinking he's honest, when in actuality he's up to something criminal with various schemes. In Batman Returns The Penguin pretended he was just looking for his parents and wanted to help the city by running for Mayor. When in actuality he was planning to murder their first born sons, and attacking their city with his Red Triangle Gang to make the Mayor look unfavourable so he could be the next Mayor.
