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.
Final Exam - S1-E1
Deliberate mistake: Cyborg, Starfire, Raven and Beast Boy are kicked out of the Tower by the HIVE, and the trio watches them from the Operations/Main Living room panorama window. But whenever Jinx, Gizmo and Mammoth are seen (before they send in the tidal wave), the same window is on their right-hand side, whereas there should be a solid wall separating Ops from the side wings.
Lightspeed - S5-E8
Deliberate mistake: In the museum, Kyd Wykkyd creates a teleport hole whose diameter is smaller than the length of the cobra staff he intends to snatch. In fact, when he takes it out of the showcase, the lower part of the staff passes right through the glass.
Deliberate mistake: Kitten and Fang's limousine is rather quite broad, as we can see when Red X pops in. But since he is using both hands to cut the car in two, he'd have to extend the natural length of his arms in order to use both X-sawblades at the same time.
Chosen answer: It is located in California, as shown in "Teen Titans: Trouble in Tokyo". Possibly San Francisco as seen in the comics.
MasterOfAll