Continuity mistake: Pantha, mistaking Cyborg for a competitor, grabs him, lifts him over her head and begins spinning him. In the shot where she is briefly seen from above, she uses only one hand, but before and after that she uses both hands to whirl him around.
Continuity mistake: With the first strum on his guitar, Punk Rocket blows the orchestra and their paraphernalia all across the stage. But after the titles have rolled and the Titans are called into action, the stage is free of the stands, music sheets, instruments, and even the conductor's pedestal which were previously scattered all about.
Continuity mistake: When Raven is ambushed by Kyd Wykkyd and Psimon, she looks at Psimon over her right shoulder (since Kyd Wykkyd sits on the canopy in front of her). But when we see the outside of the pod, Psimon hovers in the air to the left side of the pod; he even casts a glance over his right-hand shoulder, i.e. to Raven's own left side, while she keeps looking to the right.
Continuity mistake: From his fight against the imaginary Slade in the latter's old hideout, Robin sustains several injuries, including a partially swollen-shut right eye. During the last fight in the Tower's basement stairs, there is a (very brief) shot in which we can see 'Slade' leaping at Robin; in that instance, the right eye is fully open and appears not to be injured.
Continuity mistake: The high building behind the Mega Meaty Meat is revealed to be the Source's mothership when the facade peels away. But in later scenes it still has the facade on, still looking like the tall building from before.
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.
Continuity mistake: After Mae-Eye is banished back into the pie, the Titans assemble around it to ponder its fate. In the shots where we can only see their feet, they are positioned (clockwise, starting at 1 o'clock): Beast Boy, Starfire, Robin, Cyborg, Raven (who takes Silkie's place). But when we see their faces from the ground up, their positions are (taking the new perspective into account): Beast Boy, Robin, Starfire, Cyborg, Raven - on the whole meaning that Robin and Starfire switch places from one cut to the other, and back again.
Continuity mistake: In the black and white family series, Beast Boy consumes half of an enormous stack of flapjacks. But when 7-Gorn-7 (literally) gate-crashes the homely scene, the stack of pancakes he disintegrates is taller than it was before.
Bunny Raven or How to Make a Titananimal Disappear - S3-E11
Continuity mistake: Beast Boy is drawn onto the stage for a plate-juggling number. We see Mumbo balancing three plates (excluding Beast Boy) with his hands and left foot. But (again excluding Beast Boy), it's four plates getting smashed on the stage.
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.
Revolution - S3-E7
Continuity mistake: When Mad Mod activates his hypno screens in the city, there is a man among the citizens with spiky black hair and a goatee, black-rimmed glasses and a horizontal blue stripe on his shirt. When he is first seen, he has both his arms hanging down, but in the second instance where he is seen, he has somehow acquired an ice cream cone (which loses a scoop) up to his mouth.
Continuity mistake: Cyborg joins the Robin cosplay cadre, and in the garage we see him providing airflow for Beast Boy's cycle number. Look at Cyborg's right hand: first the wrist is colored green, the same as Robin's glove on his other hand, meaning that he must be wearing such on his right hand - which would be impossible without having it shredded by his hand-turned-fan. When Cyborg changes his hand back, he is not wearing a glove, but when he tries to take his turn on Robin's bike, he is suddenly wearing gloves on both hands.
Lightspeed - S5-E8
Revealing mistake: When the HIVE Five exit the museum and are intercepted by Kid Flash, Mammoth loses both his pants and the artifacts he has before KF whizzes past him. It's best seen in slow motion; at normal speed this mistake is hard to catch.
Continuity mistake: When Kitten makes Robin lead her onto the ship, Starfire is crush-gritting her teeth, then she slams her fist onto the hood of the car on her right side. When she skids into the picture, the car in question is a red sedan, but when she hits it, it suddenly is Kitten's pink Rolls Royce, which was standing in front of her (and slightly to the left) just moments before.
Continuity mistake: Hot Spot and Wildebeest get captured by the Brotherhood of Evil and flash-frozen as battle trophies. In each instance where they are seen afterward, the two are seen standing in different stances.
Plot hole: During and right after Cyborg's, Raven's and Beast Boy's fight against the mutant moths on the bridge, they contact Robin via their communicators. On at least two occasions, when their faces are seen on Robin's com and the main computer screen, the members of the trio appear not to look onto the screen of their own communicators, but at a separately mounted camera somewhere nearby.
Plot hole: After the Titans have recovered their senses, they engage Mae-Eye and her gingerbread men. Just before Cyborg and Raven are trapped in giant jars, they blast Mother Mae-Eye directly from behind. But for her to enchant them, she just turns to her left and casts her spell to her side instead of behind her.
Chosen answer: It is located in California, as shown in "Teen Titans: Trouble in Tokyo". Possibly San Francisco as seen in the comics.
MasterOfAll