Continuity mistake: Robin is chasing Red X. Red X throws a net of some kind onto Robin, then Robin says, "I'm fine. Get X. Go." and points toward Red X. Later, we find out that this was actually a hologram of Robin, when Starfire accidentally activates it again. However, this time, the hologram of Robin does not point after his dialogue.
Continuity mistake: During the Puppet King's final rehearsal (just before the title sequence), the Raven puppet has a gem on its forehead, just like the real Raven. Later in the Titans Tower, however, the gem is no longer on this puppet.
Continuity mistake: After Cyborg switches the microphones back on and Raven asks whether he could 'accidentally' leave it off, Beast Boy swells his vein. In that shot you can see the yellow marking stripe from the Titan Tower's sub hangar outside BB's canopy, however, at this time they are already in the deep sea. It's simply a repetition of an earlier scene.
Continuity mistake: When Raven summons her emotions near the end, there is a green-cloaked Raven next to the yellow-cloaked one. But when they start spinning, the cloak turns from green to red.
Continuity mistake: When Beast Boy and Aqualad each spot one of the Trident clones in the volcanic cave, they look away from each other, but when they try to point him out to the other, shouting "There he goes!", they are pointing over to the direction opposite the one each of them was just facing.
Character mistake: When the Puppet King first prepares to incinerate the Titans, Starfire (in Raven's body) and Raven (in Starfire's body) watch from a catwalk above. We can hear Starfire gasp and Raven say "No"; but curiously they do so as if they were in their respective actual bodies (i.e. Starfire's body gasps and Raven's body says "No"), whereas for most of this episode each of the girls talk with her own voice in the wrong body.
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.
Other mistake: When the probes are going off in the Titans, including Robin, Slade rips off his arm piece that houses the red button. When he does this, the probes stop. However, it would have required clicking the button again rather than just breaking it off the rest of his suit. (00:19:45)
Continuity mistake: The poster behind Beast Boy in the subway station changes colors from one shot to the next.
Final Exam - S1-E1
Continuity mistake: After the Titans are evicted from their home and grieve over their loss, before Robin re-enters, as the Titans are gazing at the ocean, Cyborg's arms are attached to him, despite having lost his right one, which is still in Gizmo's possession.
Chosen answer: It is located in California, as shown in "Teen Titans: Trouble in Tokyo". Possibly San Francisco as seen in the comics.
MasterOfAll