Batman: The Animated Series/WMG

See also WMG/DCAU

In "Perchance to Dream" Selina Kyle was actually about to offer Bruce a handjob at the office to cheer him up.
Selina visits Bruce at work because his mother called her and said Bruce "could use some cheering up." She perches on his desk and purrs, "Who better for the job than the woman you're marrying next week?" while slowly removing one of her gloves. She begins to reach out to him with her one ungloved hand before pausing and noticing that he really is upset. Putting this here rather than Radar because I'm not sure if I just have a dirty mind or if this was actually implied.

Andrea Beaumount has supernatural powers, specifically communication with the dead.
In the animated "Batman: Mask of the Phantasm" she explains that she can imagine what her deceased mother would say if she talked to her. Perhaps she didn't know it at first, but she really could talk to her loved ones in the great beyond.
 * She also claimed she was closer to her father than ever,
 * She could have used this power to bargain for other powers, or learn to develop others such as teleportation.
 * However at the end when she says "I am alone", she may have meant that she lost her communication power as a result of her crusade.

Poison Ivy and Harley Quinn are not lesbians
I realize it's far-fetched and I don't have any evidence to back it up, but I get the feeling there is at least a one in a million chance that they are just friends. Now if you'll excuse me, there is a mob of angry fanboys outside my door with torches and pitchforks.
 * Perhaps Harley Quinn is bisexual. She has a serious crush on the Joker, who is male, and had grandchildren in Batman Beyond (though her kid may have been in-vitro or adopted).
 * Harley suffers from Single Target Sexuality. She is hopelessly obsessed with Mistah' J. When he throws her out (literally) she immediately focuses on the very next person to show her kindness: Ivy.
 * Word of God has stated that Harley Quinn was in a, erm, physical relationship with Ivy in the episode Harley And Ivy (It just couldn't be explicitly stated due to the series being a kids' show). So, Harley is bisexual (or at the very least bicurious). Her heart's just set on The Joker, though.
 * Links or it didn't happen.

The moral of Mask of the Phantasm is that sexism is bad.
If Bruce (having already learned Andrea was his equal if not better at martial arts) hadn't assumed she would "always be at home waiting for me" but thought of her as a possible partner, he wouldn't have felt forced to choose between love and crime-fighting. Most likely, he would have shared his secret with her earlier; maybe they would have been able to save her father from the mob together. Finding a woman who could handle his secret if not fight alongside him (instead of one whose worry would be a burden) never occurred to him, and that is the only reason he ended up alone/resigned himself to being alone.
 * To be fair, the only time Andrea's by his side during a fight (when they run into the bikers harassing the guy with the box full of jewlery) she just stands on the sidelines pulling concerned faces and actually distracts him during the fight, leading to him taking a baseball bat to the ribs with enough force that the bat breaks. Considering how her attempt to fight of Salvatore's men when they arrive to threaten her father results in one hiya noise before she gets a taste of Standard Female Grab Area, it seems that Andrea's status as a potential partner in crimefighting wasn't really viable until after her dad got killed, which presumably led her to supplement her self defence class training with Bruce-style Training From Hell.

Killer Croc's theory about Batman being a Robot isn't just him being stupid.
Remember it actually did happen in one episode! Croc probably had an offscreen encounter with the Batman Android, and that's why he thinks Batman could be a robot.
 * Meh, details...
 * Remember though, Joker told him not to bring it up "again", so this isn't the first time it's come up.
 * Remember though, Joker told him not to bring it up "again", so this isn't the first time it's come up.

The girl with red hair in "Legends of the Dark Knight" is actually Carrie Kelly
She fits the physical description from the books, and how else would she know about the events in TDKR? She time traveled or dimension-hopped or something.
 * She is Carrie Kelley. But she was never Robin, and her story never happened, it's just her own view of what Batman is like. She likes to put herself in the story; and made herself wrong when she thought Robin is a girl.

Those guys in the opening sequence didn't do anything wrong.
There was an explosion and they ran away, took it to a bit of an extreme by climbing a roof, then ran into Batman who was probably just scowling at the city from that particular roof top. He looks at them like he's going to attack, so they pull their guns to defend themselves. The rest is history.
 * They pulled guns. On BATMAN. If that's not doing something wrong, I dunno what is.
 * They tried to pull a bank robbery which had gone wrong.
 * Maybe they were working for the bank owner, blowing up the bank to collect insurance.
 * Which I believe is legal in Gotham.

Matt's story about his uncle meeting Batman and Robin did happen.
Only it happened during Batman (and Robin)'s early crimefighting career. It happened not too soon after Joker first appeared. Batman also wore the "Golden Age" costume in the flashback of "Robin's Reckoning". The Robin in the flashback was Dick Grayson, soon after he found out Bruce is Batman in the flashback. His uncle was half-asleep at the time, which explains the Art Shift and the cheesy dialogues, since that's how he recalls.

Dr. Joan Leland is doing drugs.
She's the most mellow Arkham employee seen in any medium. She's definately on something. My vote is either a lot of pot or opium.