2040:
Why 2040?
Because in the second year of Terry McGinnis's reign as Batman he meets the infiltration unit Zeta:
Batman Beyond episode "Zeta": "Zeta was on a long term assignment, infiltrating a terrorist group; six days ago it went renegade." - Agent Bennet to Police Commissioner Barbara Gordon.
Zeta later had his own series:
The Zeta Project episode "Quality Time": "NSA File Review. Subject: Renegade Infiltration Unit Zeta. Unit Zeta went renegade August 5th, 2041, during the infiltration of suspected terrorist group Brother's Day."
Six Days after August 5, 2041 is August 11, 2041. This information is what grounded Batman Beyond in the 2040's.
2041 (Year 2 of Batman Beyond) minus 1 = 2040 (Year 1 of Batman Beyond).
Want more evidence?
In the Year 1 Batman Beyond episode "Meltdown", Gotham reencounters a face from the past when Mr. Freeze returns.
"I've been like this for nearly 50 years, and I haven't aged a single day." - Victor Fries to Dr. Lake.
The 'nearly 50 years' quote is chillingly accurate; per this timeline the accident that changed Victor Fries into Mr. Freeze took place in 1991, 49 years before this installment. It all fits.
Why this order?
Because Batman Beyond makes the most sense in the order the episodes were produced; not the order they aired, so I'm staying as close to production order as I can, while simultaneously allowing for change based on random story variables.
1x01 Rebirth, Part I
1x02 Rebirth, Part II
Terry McGinnis meets Bruce Wayne for the first time and becomes the new Batman.
Chelsea Cunningham introduced.
Mr. Fixx is introduced in Part I and apparently dispatched in Part II.
Barbara Gordon (now Police Commissioner) is mentioned in Part II.
Marry McGinnis introduced.
Matt McGinnis introduced.
Warren McGinnis is introduced (and killed) in Part I.
Nelson Nash introduced.
Derek Powers / Blight introduced.
Dana Tan introduced.
Bunny Vreeland, an allusion to Veronica Vreeland, is featured in the 2020 set prologue of Part I.
Though many DCAU characters made their final appearances in the previous episode ("Destroyer"), there are several returning characters, mentions & references to things past to be found in Batman Beyond to satisfy hardcore continuity junkies.
Terry McGinnis / Batman, older Bruce, his futuristic Gotham City & his faithful dog Ace are reintroduced here after first appearing in the Static Shock episode "Future Shock", and returning in the alternate futures of the JLU episodes "The Once and Future Thing, Part I: Weird Western Tales" & "The Once and Future Thing, Part II: Time Warped".
Terry and his classmates (Chelsea, Nelson & Dana) attend Hamilton Hill High School. Hamilton Hill was the Mayor of Gotham City during Batman: The Animated Series:
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"Gotham rolled out the red carpet today for Kaznian Minister of Commerce Vilmos Egans." - Reporter (Rebirth, Part II)
Kaznia was a recurring fictional country in Superman: The Animated Series ("The Last Son of Krypton, Part II", "The Last Son of Krypton, Part III"), Batman: Mystery of the Batwoman, Justice League ("Maid of Honor, Part I", "Maid of Honor, Part II", "Starcrossed, Part I") & Justice League Unlimited ("Hawk and Dove", "The Great Brain Robbery").
There are allusions to Bruce's former allies: Robin (Tim Drake), Batgirl (Barbara Gordon) & Nightwing (Dick Grayson)...
old adventures featuring: the Bat Cave, the Batmobile, the Batwing, the Bat Computer...
And old enemies: Two-Face, Calendar Girl, Harley Quinn, The Joker, Scarface / The Ventriloquist.
1st appearance of a different gang of Jokerz (criminal clowns inspired by the original Joker) than had appeared previously in the JLU episodes; these new Jokerz are not always named but several recur throughout the series.
The Joker on the far left is Scab. The one driving the motorcycle on the far right is Coe. The Joker look-alike (sometimes credited as the Jokerz Leader in the end credits) on the pink bike is referred to as J-Man in "Joyride".
Also, Mr. Fixx uses electrified knuckles just as Batman did in the Justice League episode "Secret Origins, Part II" & the JLU installment "Destroyer":
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1x03 Black Out
Inque introduced.
1st Appearance of the new Batmobile.
Derek Powers / Blight returns.
"Black Out" is a nearly direct continuation of "Rebirth, Part II", with many references to the previous episodes...plus tons of DCAU continuity.
Barbara Gordon (now Commissioner) reintroduced and James Gordon referenced:
Bruce's parents (Thomas & Martha Wayne) appear in a painting at Wayne Manor:
There are references to Lucius Fox & his family in this episode, linking them to the Foxteca corporation being targeted in this episode by Derek Powers and Inque:
"Keep your hands off Foxteca." "The Foxes were a valued part of this company for years." - Bruce Wayne to Derek Powers
"Lucius Jr. was still Vice President when I took over." - Derek Powers to Bruce Wayne
Allusions are made to Mr. Freeze, Riddler, Robin, Batgirl, Nightwing, Two-Face, Joker, Mad Hatter, Harley Quinn, Calendar Girl, Ventriloquist / Scarface, Catwoman, Penguin, Firefly & the Grey Ghost:
Also, some of those nameless Jokerz reappear here:
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1x04 Golem
Willie Watt introduced.
Blade Thompson introduced.
1st use of the camouflage feature on the Bat Suit.
A few recurring Jokerz return.
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1x09 The Winning Edge
Final appearance of Bane.
The camouflage function on the Bat Suit (introduced in previous episode: "Golem") reappears here.
The Hamilton High sporting team introduced in "Black Out" is expanded upon here.
Several recurring Jokerz return as well:
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1x08 Dead Man's Hand
Terry's partnership with Bruce Wayne puts his relationship with Dana on hold; a plot point that has been building from the start of the series.
A new version of The Royal Flush Gang introduced:
Queen
Ace
King
10 / Melanie Walker
Jack
"They'll be back. We've got history; they and I. The Royal Flush Gang's been around a long time. They're a family. They bring in new members, sons, daughters, husbands, wives, as the older ones retire or go to prison. They think they're better than everyone else; the aristocrats of crime." - Bruce Wayne to Terry McGinnis.
"Years ago when I was your age he broke up this gang for awhile. He outsmarted us; humiliated us. I've been waiting years to pay him back." - King speaking to Jack about Batman.
It's possible this iteration of The Royal Flush Gang was broken up before the one introduced in Justice League (it's implied in JLU's "Epilogue" that the Justice League version might not have been the first). It's also possible that this version stems from the one introduced in Justice League's "Wild Cards, Part I" & "Wild Cards, Part II"; they were also referenced in JLU's "Fearful Symmetry".
Terry's relationship with 10 / Melanie mirrors the relationship between Bruce & Catwoman / Selina.
"Let me tell you about a woman named Selina Kyle." - Bruce Wayne speaking to Terry McGinnis about Catwoman.
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1x06 Heroes
Barbara Gordon appears.
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1x10 Spellbound
Ira Billings / Spellbinder introduced.
Jim Tate / Armory introduced.
Barbara Gordon appears. It's implied that she figures out that Terry is the new Batman in this episode.
Terry makes a veiled reference to Robin I / Nightwing, Robin II & Batgirl:
"Guess you're the expert on troubled kids; you collect them, right?" - Terry McGinnis to Bruce Wayne.
Reference is made to the Princess Audrey dress collection; a reference to Kaznian Princess Audrey who was featured in the Justice League episodes "Maid of Honor, Part I" & "Maid of Honor, Part II". The posters for the Princess Audrey Collection feature a woman who doesn't look much like the Audrey from Justice League, but it's possible that Audrey dyed her hair at some point in her life, or that the photos for the collection are of a model wearing the Princess's famous dresses.
Dick Grayson is later referenced again:
"Who's D G?" - Terry to Bruce.
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1x07 Shriek
Derek Powers / Blight returns.
Walter Shreeve / Shriek introduced.
Bruce & Terry visit Park Row, the neighborhood where Bruce's parents were killed. While there, Bruce spots an old wanted poster featuring The Joker:
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1x12 A Touch of Curare
Sam Young (Barbara's husband) introduced.
1st mention of Terry's time in Juvie Hall. This explains why he's still in High School at age 19. The circumstances of the Juivie Hall incident are revealed in the 2nd Year story "Big Time".
Barbara's history as Batgirl and her relationships with Dick Grayson & Bruce are discussed.
"I see you sewed up the bullet holes." - Barbara Gordon.
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Terry: "So you and Dick Grayson, like, dated?"
Barbara: "In College. Puppy Love. Later on we just never talked about it. Dick finally got fed up living in Batman's shadow; he decided to leave; he was hurt when I decided to stay behind with Bruce."
Terry: "As his partner...his girlfriend? Whoa."
Barbara: "On the street it was like ballet. We were the perfect duo. But for Bruce...Batman...there was nothing but the street. Eventually that gets old. Time comes when you have to hang up the cape. But Bruce wouldn't...or couldn't...so I left and never looked back. No, I don't hate him. I hate what he's become. Such a great man...so alone."
A romantic element to the Batman / Batgirl relationship (at least on Barbara's end) was hinted at in "Batman: Mystery of the Batwoman". It's possible that it never went anywhere. There's nothing in the shows that said they did or did not become a couple.
Jim Gordon is also referenced:
"I've looked the other way so far, but I'm not my father." - Barbara Gordon to Bruce Wayne & Terry McGinnis.
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1x11 Disappearing Inque
Inque returns.
A new rendition of the theme to Batman: The Animated Series is heard.
"It's taken me what? 6 months just to get you to show me around the cave?" - Terry to Bruce.
"What is he? Your father? Grandfather?" - Inque to Terry McGinnis.
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1x05 Meltdown
Derek Powers / Blight returns; Blight encounters Batman.
Final appearance of Victor Fries / Mr. Freeze.
"I've been like this for nearly 50 years, and I haven't aged a single day." - Victor Fries to Dr. Lake.
Per this timeline the accident that changed Victor Fries into Mr. Freeze took place in 1991, 49 years before this installment.
This episode features several scenes with snow and ice on display so it seemed best to place it as late in the season as possible (plus Derek Powers dialogue about his condition worsening seems to lend itself to taking place as late in the season as possible), but even with that weather, they speak about a heat wave of over 70 degrees, which reinforces my theory of extremely mild Winters in Gotham City.
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1x13 Ascension
Paxton Powers introduced.
Final appearance of Derek Powers / Blight.
Final appearance of The Bat-Signal.
"Next time use e-mail." - Batman