Commissioner Gordon laments to Chief O'Hara that "it was a sad day indeed when the word 'parole' was coined." This is an ironic utterance, given that he castigated Robin for expressing the same sentiment regarding The Penguin in Fine Feathered Finks (1966).
When Batman punches the Mad Hatter in the face his glasses fly off his face. In the next shot he removes them and places them on the statue.
Aunt Harriet seeks Bruce's advice on what tea to serve for a gourmet tea tasting, saying she can't decide whether to start with oolong or pekoe. A gourmet-level tea taster should know that pekoe refers to the size of tea leaves, not a varietal.
Obvious stunt man of Robin during the fight with the bad guys.
Given that the Mad Hatter's kidnapping victims sat on the jury that sent him to prison, it seems odd that none of them recognize him on sight.