Batman and Robin try to prevent the Penguin from stealing some priceless jewels, only to be framed for their attempted theft by the Penguin himself. The Penguin used this very trick (with a jade idol) against them in Detective Comics #58 (1941), his first appearance.
Batman & Robin are seen driving the Batmobile in front of a process screen, and the city they are driving through is West Berlin.
Alfred claims to be from the insurance company Floyd's of Dublin. This is a reference to Lloyd's of London, an insurance and reinsurance market founded in 1686.
"This picture of Sophia's jewels" that Batman points to in the bat cave is clearly a head/publicity shot of actress Kathleen Crowley who plays Sophia Starr in the episode.
The establishing shot shows the Booth Theatre located at 222 West 45th Street in Manhattan. Opened in 1913, it was named after the acclaimed 19th Century Shakespearean actor Edwin Booth, the elder brother of John Wilkes Booth.