The background seen in the Batcave, in Part II, is the one used on Batman Beyond (1999), as one can see Terry McGinnis's Batsuit right next to the Nightwing one (though it has a yellow emblem, instead of a red one). Due to the "time period" of said episode, the Beyond Batsuit shouldn't exist yet.
When the Justice League escapes into a building, Wonder Woman crumples the door. When the League closes the door again, it appears to be undamaged.
The Thanagarians confiscate Green Lantern's ring, but leave Batman his utility belt.
Hawkgirl is not present in the "secret identity" scene, but she somehow deduces that Bruce Wayne is Batman and that the Justice League is regrouping in the Batcave.