Continuity mistake: In the super-flu episode, the head master says he wants to beat the previous record of no sick days by beating the previous headmaster who had no sick days from 1979 to 1999. However, later he says he only has to last one more day. How? He's only worked there nine years at the most, as we know it's set in the present.
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.
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.
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: 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.
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.
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 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.
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: The poster behind Beast Boy in the subway station changes colors from one shot to the next.
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: When Raven telekinetically reassembles the broken chime bead necklace, it has about nine beads and is rather tight, but before and after that the necklaces feature about 13 or 14 beads and are wide enough to fit around the others' necks.
Continuity mistake: Within the timestream, Starfire rips off Warp's vortex regulator with her left hand. She still has it in her hand when she first shields her face with her left arm, but as we see Warp dropping out of the timestream and Starfire following right afterwards, both of her hands are empty.
Continuity mistake: After Warp just barely managed to fend off Nightwing's grenades, he notices Nightwing's shape leaping at him. In that shot, before the scene where Warp sinks into the ground, the socket for his vortex regulator is glowing blue instead of red.
Plot hole: The alternate future Cyborg must stay connected to a large and heavy generator, which stands in the Titan Tower's common room, in order to remain functioning. But as we can later see, the power cables have a rather limited length, and the device is obviously too heavy to move easily. So how comes that Cyborg can roam the Tower and come through the common room's main door, where he appears when he confronts Starfire, without even any of the thick cables showing?
Continuity mistake: Starfire intercepts Soto's ship upon take-off and pushes it back to Earth. But when Soto proceeds to activate the lift-off thrusters, look at the UFO's window: the canopy of treetops moves in a fashion which indicates that the ship is currently moving up, not down.
Fear Itself - S2-E5
Continuity mistake: When the Wicked Scary Monster first reveals itself in the Titan's Tower, we see the Titans huddled together in chibi-form after the commercial break. At first we see the Titans cowering behind Robin, who is standing in the middle, but when we see the Monster again up front, suddenly Starfire has taken the center and Robin stands between her and Beast Boy.
Fear Itself - S2-E5
Continuity mistake: The animated video shelf which goes after Beast Boy uses red and grey DVD cases as eyes and teeth. When Beast Boy roars at it as a T-Rex, the shelf loses its "eyes" and "teeth" out of fright, but when Beast Boy charges into it, it suddenly has them all back on.
Fear Itself - S2-E5
Continuity mistake: After the video rental clerk shoves the Wicked Scary DVD into Beast Boy's face, the scene fades to the evidence room where Robin is depositing Control Freak's remote. In the showcase to the left which holds the masks of Slade's robots, we also see some of the Puppet King's Titan puppets and his soul-switching control, which got crisped in blue fire in first season's "Switch"; therefore it should not be on display. (Switch to slow run to detect it; it's rather difficult to catch on normal speed.).
Chosen answer: It is located in California, as shown in "Teen Titans: Trouble in Tokyo". Possibly San Francisco as seen in the comics.
MasterOfAll