The Ink Well that everyone emerges from gushes ink and paint instead of normal water. Weird, but hey, fits the setting, right? Another, similar quirk is that everyone's blood is replaced with black ink, which... wait a sec.
It's heavily implied that whenever somebody arrives in the City, their Canon is changed and they actually are absent in their world — it's not just an automatic case of Year Inside, Hour Outside or Narnia Time. This raises questions about the state of the universe left behind, especially when it comes to heroes with grand quests or heroic deeds to perform.
Tigress is only a child when she arrives, having been plucked from her world shortly after Shifu first offered to train her. So the little girl he was about to take in as a pupil and adopted daughter just vanished without a trace...
Leads to a bit of an unsettling implication regarding the pony cast - Rarity and Twilight Sparkle never noticed Fluttershy missing, which implies that the pony cast are from not one, but two seperate 'continuities' that just suddenly had one or more of the Elements of Harmony just up and vanish. Given that Discord is very much not a statue, it's entirely possible that his presence is from the version of Equestria where Fluttershy went missing.
Optimus Prime points out to Soundwave that if Megatron arrives in Ink City, that would throw the Decepticons back home into a Succession Crisis with everyone scheming and jockeying to fill the void. Left unspoken is the fact that the Autobots of their world are currently leaderless themselves...
And then Megatron does show up.
Along with themselves, new residents may bring along a familiar location from their homeworld, such as their home, an office, or someplace similar. Much like the characters themselves, these places vanish as well.
Dot flat-out tells Yakko that when he disappeared, so did the Water Tower. Eventually, Wakko disappeared without a trace as well, leaving her behind to wonder where her brothers went. While she was 'fortunate' enough to end up in the City herself as well and have those questions answered...
When Ichigo arrived, she brought along one of her favorite rolling places, the Ikebana Flower Garden from We ♥ Katamari. In-game, the area is filled with deer, fairies and other fauna along with plenty of flora. Only the latter made the transition; not a single trace of its original inhabitants remain.
Po showed up with Ping's Noodle Shop. Meaning his father isn't just dealing with his son disappearing, but his home and the rest of his life's work.
Tigress brought along the Bao Gu Orphanage.
Aile brought along the airship that acts as the Guardians' home base. Which they were all inside at the point of her abduction.
The ink monsters are implied to be empty shells who haven't yet found a 'blueprint' to give them a more defined form or personality. This raises all sorts of further questions about the characters themselves — are they the originals, simply given inky blood and the ability to regenerate in the Ink Well, or mere copies? And if the latter, why did the originals still vanish from their worlds?
Another detail with terrifying implications: during the Superboat arc, some of the ink monsters mimic the voices of people who left the City — and, after Heloise is killed, her voice as well. Of course, it's fully possible that they're not just mimicking the departed, but...
When a character leaves the City, this can apply to the last thing they were seen doing. For instance, during the World Split, Toothless was last seen in the throes of Split-induced Body Horror, and Fluttershy had a broken leg...
If a character is dropped, and re-apped with no memory of the City and an unchanged canon, what happened to the original? Is that character effectively erased with a functional clone installed?
Gonzo's displayed awareness of his puppeteer, Dave Goelz, and even shown him off on one occasion. Goelz (along with arm rods and Gonzo's status as a puppet) appeared only faintly. Is he trapped in some horrible limbo between the 'real' world and Ink City? Is part of his soul attatched to Gonzo? Who knows.