"The Big Dummy" sees Bruce putting off a date with a woman named Becky, voiced by Jennifer Hale. It isn't the first time a character voiced by Hale served as a love interest to a superhero voiced by Rino Romano, but in thoseothercases, they did hook up and actually had a relationship.
Executive Meddling - Some of the intellectual property from Batman was being used in multiple adaptations (all owned by the Warner Brothers, however). Not wanting to create conflict between different adaptations' interpretations of characters, some things were off-limits for the writing staff. Here are specific examples:
Robin was forbidden from appearing until Teen Titans was canceled, meaning Batgirl actually becomes a sidekick first, which makes for an interesting mythology shake-up and promotes her from the usual third-fiddle.
Some of the villains used in the The Dark Knight Saga, most notably Scarecrow and Two-Face, were also forbidden from appearing. Clayface was used in place of Two-Face for the "best friend turned into a criminal" schtick. The episode "Strange New World" was written to introduce Scarecrow, but once the writing staff found out that he was still off-limits, they opted to go with Professor Hugo Strange instead.
All of the above is very ironic, considering the "Bat-Embargo" this series imposed onto Justice League Unlimited (another reason for the dislike The Batman gets).
What Could Have Been - As mentioned in Executive Meddling, the original idea of what became Strange New World, the villain was the Scarecrow, but as he was still off-limits, he was replaced with Hugo Strange. However, given the episode's plot, it was probably for the best as he'd have given the twist away. Likewise, a proposed but rejected idea of a follow-up DTV to The Batman VS. Dracula would be an adaption of Hush. Likewise, the villain on Rumors was originally supposed to have been Hush, too.