Watching the opening cutscene of Lego Batman, you might wonder what a perfectly sane catburglar like Catwoman was doing in Arkham Asylum, as opposed to a regular prison. Upon completing her level in the game (at the end of which Batman captures her by putting out a saucer of milk and she just can't resist lapping it up like a cat), it becomes clear: this version of Catwoman thinks she is actually a cat.
In Lego Batman, the extras are unlocked by finding red power bricks in the Villain levels. The first 5 are all score multipliers, and are all found in the Riddler levels... because Riddler's plan is to rob the gold reserve. Of course his extras would all be about money and how to get it easily
In LEGO Batman 2, every returning villain (except Joker and Scarecrow) is a Degraded Boss. This makes sense when you think about it: in the first game, the villains had a plan to break out, so they already had equipment, gangs, and hideouts ready for them once they escaped. In the sequel, they escaped because Joker and Lex set them loose while escaping to keep Batman busy, so they were completely unprepared.
Of course Batman's space suit is white. Helps him stay visible in the darkness of space, just like real astronauts.
In LEGO Batman 3, why would Cheetah, after being captured and tied up, insult Wonder Woman on her outfit and her relationship with Superman? Because she's being catty.
Of course the rivers on Ysmault are filled with jam. Lego characters don't have blood.
In Super Villains, many of the Customizable Player Character's actions make sense following The Reveal, even though most of it is left implied: They are, in fact, from Earth Three, like the Crime Syndicate. They came to Earth One to break in to the AMAZO Project so that they could start gaining powers to fight back, which also explains why they were so quickly willing to join the villains in resisting. However, the reason for vengeance against the Crime Syndicate leads to a piece of Fridge horror...
The part leading to Fridge Horror is Jossed if you read their file after the story is completed. They can't speak because their empowering had the side effect of making them unable to talk.
In Super Villains, Scarecrow gushes over getting to rescue Sinestro because he's his biggest fan. Since the Sinestro Corps' rings are powered by fear and Jonathan Crane is all about using fear gas on people, of course he'd be a Sinestro fanboy.
In Lego Batman one of the Joker's unlockable outfits is a tropical tourist's garb, with a purple fedora, Hawaiian shirt and a camera. It's a funky little ensemble, until you realize that it was what he was wearing when he shot and crippled Barbara Gordon.
Croc says Dr. Fate's helmet was in his stomach from "yesterday's lunch". Poor Kent Nelson...
But he's a playable character in the game you unlock, most likely he was trying to freak Robin out.
The statue of Abin Sur at the Indigo Tribe might not make any sense in Beyond Gotham, but comics fans will know that it's because Indigo-1 killed his daughter. That's right, as per the comics Indigo-1 is a child-murderer as well as a total sociopath.
In Super Villains, following the twist in Fridge Brilliance, is why the Custom PC never speaks. Whatever the Crime Syndicate did to merit payback at the level the Custom is willing to go to, it either physically or mentally rendered the Custom unable to speak from the trauma.
Presumably it is a mental block as the character does make sounds like grunting during certain game play actions so it's either mental or Gameplay/Story Segregation