In Big Barda's closet, you can see the costume that belongs to her husband, Scott Free aka "Mr. Miracle".
When Kara and Superman are speaking Kryptonian, they actually speak Esperanto, an internationally constructed language similar to German.
This takes place after the events of Superman/Batman: Public Enemies (2009), as it mentions the impeachment of President Luthor and the giant kryptonite meteor that threatened the Earth in that movie.
Coincidentally, this movie was released the same week that Clark and Kara teamed up again to fight Darkseid on the WB's Smallville (2001). However, the plot of the Smallville episode was the reverse of what it was in the movie, where instead of Clark saving Kara from Darkseid, it was the other way around.
This marks the third time that Superman, Batman, and Wonder Woman have been teamed up together in an animated movie. The first was Justice League: New Frontier, and the second was Crisis on Two Earths. It is the first time that they were featured without any of the other founding members of the Justice League.