This episode marks the chronological end of the Bruce Timm "Batman" stories. The last line, "Did you see that?" is the same as the first line of On Leather Wings (1992), the first episode of Batman: The Animated Series (1992). More specifically, the episode is also intended to be a de facto series finale for the series, Batman Beyond (1999).
According to writer Dwayne McDuffie, Bruce, as the world's greatest detective, was aware that Terry and Matt are his genetic offspring some point after Terry assumed the role of Batman and realized the machination of Amanda Waller and Project Cadmus, but would never bring it up as he wanted Terry to be his own man, and out of respect for Warren McGinnis as well since he was the one who raised him since birth.
The night of Terry's would-be accident, he has just finished watching The Gray Ghost Strikes. The Gray Ghost is a childhood hero of Bruce Wayne, who appeared in Batman the Animated Series and was voiced by Adam West, who played Batman in the 60s tv series.
Waller's assassin is Andrea Beaumont/The Phantasm, the title character of the film Batman: Mask of the Phantasm (1993).
Dwayne McDuffie confirms the setting to be 15 years after the end of Batman Beyond (1999), which. Bruce Timm gives this as 50 (not 40 as some claimed) years in the future from when the audience is watching it.