Tipton Tea from "Tempest in a Teacup" might not make much sense past Tipton Industries having owned quite a few random properties. But if you think back to the "Boston Tea Party" episode of The Suite Life of Zack and Cody, back in the 1700s, Lord Tipton owned a tea ship and was having tea shipped to America a few hundred years ago.
The reason Mr. Moseby ended up managing the New York Tipton? That was where they were in the final episode of The Suite Life on Deck, and therefore the last place Zack and Cody would think to look for him.
But, in his phone call to Cody, after Mr. Moseby mentioned Jessie's uncanny similarity to Bailey, Cody said that he wanted to come over and see for himself. That seems to imply that Cody does know where Mr. Moseby works.
How did Christina find out about Bertram's laziness? Obviously through the same surveillance system used for Jessie.
In "World Wide Web of Lies," Mrs. Ross tells Jessie that she's under 24 hour surveillance, to the point where they know of Jessie's sleep-eating (which Jessie herself doesn't even know).
In the Girl Scouts expy episode, Emma says that she can see her bedroom from where she and the Scouts are camping in Central Park, then remarking that she "really needs to get blinds". Keep in mind that at this point in the series she would be, at most, 16 years old (probably only 15), and that if she can see her bedroom from Central Park, other people can probably see her on the street... And that most people at some point get dressed in their bedroom...
Every time we see Creepy Connie, she seems to be more and more insane. In "Creepy Connie Comes A Callin'", she was mostly just a Creepy Child, and the worst she did was decapitate a stuffed koala, which, while creepy, isn't nearly as bad as what she did in "Creepy Connie's Curtain Call," where she grievously injured several people and threatened Luke with a flamethrower, just to get to kiss Luke. And then, in "Creepy Connie 3: The Creepening," she goes so far as to forcibly marry Luke and kidnap anyone getting in the way to act as "witnesses" to the wedding. While her mental state was never fantastic to begin with, you have to wonder how much further whatever is left of her sanity will deteriorate...
Jessie states in "Tempest in a Teacup" that her prom ended with her embarrassment at her Senior Prom. Prom is typically in May and she graduated in June. She arrives in New York in what appears to mid to late summer or early fall. She either left very soon after graduating and didn't get to New York City months later, or had many more of her wrecked relationships after graduating but before packing up and leaving for New York. Either way, while she didn't have the best life in Fort Hood, Tx, the Prom incident is more than likely what caused her to leave town. Going to New York is just a side bonus. And why didn't she choose Los Angeles. Make you wonder about her, not to mention What Might Have Been had Jessie gone west.
One episode has Jessie flat-out state she went to New York to work in theatre....and bemoans that she was being artsy and "too good" for Los Angeles....