Mrs. Cooper has to be introduced to the Penguin, but she has met him twice before in "Batman" (1966) {The Penguin's Nest (#2.27)}_ and "Batman" (1966) {The Bird's Last Jest (#2.28)}_, to the point of even getting involved in the latter episode's Bat-fight.
Penguin's prop man tells him that he has the 24,000 gallons of milk ordered for the shooting of Scene 12. Later on Penguin points to the milk and says the amount is 23,000 quarts.
After Batman and Robin are fastened to the catapult, Penguin suggests they go to a "better advantage point" to view the demise of Batman and Robin, when he should have said "better vantage point".
The series repeatedly establishes that Batman & Robin are "duly-deputised officers of the law", and as such, have official immunity for any acts taken in the line of duty. Therefore, the Penguin could not sue them for assault, even if they were in the wrong, and could not have them arrested. The city would be likewise protected from being sued for failing to protect Penguin's set.