Reality Subtext: Andrea is named after Andrea Romano, the voice casting director for the series. The entire romance plot came about because of Kevin Conroy ad-libbing an "Oh! Andrea" after a series of grunts. It was originally intended to be Batman getting punched, but the ad-lib made it sound a little different.
The fighting style Bruce was shown practicing was very close to Taekwondo, despite him calling it "Jui Jitsu". The move Andrea performed on him, however, was from Jui Jitsu.