Continuity mistake: Right after Beastboy "pulls the red candy cane thingamahoozit", and the T-ship flies toward the screen, Cyborg's hands and forearms are visible, even though they aren't found until the end of the episode.
Deliberate mistake: When the T-Ship is hit from the blast from the exploding space station, it spins around for a while before it re-stabilizes. Just before it does so, look out of Raven's canopy: the background outside with the stars and even a planet spin as the ship does, whereas realistically it should remain calm and stable.
Chosen answer: It is located in California, as shown in "Teen Titans: Trouble in Tokyo". Possibly San Francisco as seen in the comics.
MasterOfAll