This fic is getting richer and deeper! So now Diana Prince has showed up, Superman's spaceship is possibly coming to light, and Batman and Superman have teamed up. Great start!

Quote
“It seems like Batman always shows up when there’s a disaster,” said Lois. “How is it that you’re able to contact him?”

“We use the Bat-Signal, Miss Lane," said Commissioner Gordon.
Reading this bit put me in mind of the "Law and the Multiverse" blog, where lawyers discuss what legal liability the superheroes would be exposed to.

In this case, the discussion is about "Since Commissioner Gordon and the Gotham PD are able to call Batman and in effect, deputize him, is Batman held to the the laws that pertain to police conduct?" (The lawyers explain it much more fluently.)

Thanks to whoever posted the link to this blog in the first place on the L&C Boards - I forgot who it was, and in what thread, but the blog has given hours of entertainment!