The name "Baby Jane Towser" is a parody of Baby Jane Holzer, a socialite who was part of Andy Warhol's circle and was prominent in the NY art scene during that era. In fact, Holzer acted in Batman Dracula, Warhol's 1964 tribute to the character.
The Joker's vandalism of art in this episode is echoed in Batman (1989), in the scene where he first meets Vicki Vale.
After the Joker paints Batman's costume, he doodles what appears to be a cursive J on the Bat emblem. But in the next scene, in Commissioner Gordon's office, the cursive has been replaced with a printed capital J.
The four other artists in the art contest (besides the Joker) Vincent Van Gauche, Jackson Potluck, Leonardo Da Vinski and Pablo Pincus were obviously takeoffs on the real artists, the Dutch Vincent Van Gogh, the American Jackson Pollock, the Italian Leonarda Da Vinci and the Spaniard Pablo Picasso. However, while Pollock and Picasso did work in abstract art, like their imitators here, Van Gogh dealt more with a form of impressionism, and the long dead Da Vinci was a representational artist only, unlike their Batman counterparts.
At the time this episode was filmed, modern art (Op, Pop, etc) was in vogue, with artists like Andy Warhol and David Hockney leading the movement. This vignette might be a subtle (or not so subtle) send up of that whole 'mod' scene. Pop artists such as Warhol and especially Roy Liechtenstein recreated comic book panels in their artwork, exaggerating the Ben-Day dots used in the four-color printing process used for comic books at the time. As well, Warhol directed a camp sendup called Batman Dracula in 1964, and did a photo shoot dressed as Robin (the model Nico posed as Batman).