Some flirting.

Bruce Wayne and Miss Kitka kiss a few times.

During the scene In the bar full of "riff-raff," there was a picture on the wall that had a topless woman in it. Her breasts, including her nipples were briefly visible.

There's a fight in a hotel room between Bruce Wayne and several villains, but he's knocked out and kidnapped.

There's a fight in the villains' lair between Bruce Wayne and the villains, and he manages to escape.

There's a brief fight in the Batcave as Batman and Robin take on several men, and they stand on the Batmobile and kick them.

An exploding shark made by the villains bites Batman's leg and hangs onto it as he hangs from a helicopter's ladder in the beginning, and he kicks the shark off after using shark repellant, and it falls and explodes on the water.

Several men are reduced to piles of dust by a ray gun. They are reversed back to normal eventually.

Batman rushes to get rid of a bomb and eventually throws it over the side of a dock and it explodes.

There's a large fight on a boat in the end, with lots of non-brutal punching and kicking, and many people fall into the water.

Penguin calls Catwoman a floozy at one point.

The Penguin smokes cigarettes throughout the movie. Alcohol is shown briefly during scenes in the tavern that serves as the villains' hideout. A man and a woman drink some wine while having dinner.

Six of the villains' henchmen are killed: five simply disappear during a fight scene, while another is thrown through an open window out into the sea where he collides with an "exploding octopus." There are two scenes where men are turned into piles of colored dust when the villains use a "dehydrating machine" on them.