While it's purely casual, in the Finnish dub Joker says that the Phantom looks like Darth Vader. Coincidence?
Box Office Bomb: Due to a lack of advertising, the movie bombed hard during its theatrical run. This didn't last forever, though, as a certain trope to be seen below indicates...
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.
Screwed by the Network: The film did not have a pre-release screening for critics, which hurt it badly, since when a production company does that, it indicates that the film is probably awful. The reviews that did come out were generally positive, but they were on a Saturday, instead of the launch day, and generally, movie reviews on a Saturday are passed over by readers.
The film was going to be completely computer generated, but that was dropped for traditional cel-animation. The CG buildings during the opening credits are an artifact from that plan.
The movie was originally planned as the series finale for Batman: The Animated Series, which explains why Joker seemingly dies at the end. It was also originally going to be a two-parter called "Masks" featuring Batman Year Two's villain Reaper, with Batman's origin being a standalone ep called "Vigil."
You Look Familiar: Andrea is voiced by Dana Delany, who later became more famous as the voice of Lois Lane in Superman: The Animated Series. In fact, Word of God has stated that it was her stellar performance here that caused them to pursue her for the role of Lois in the first place. Bruce even had a brief relationship with Lois.
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.