Plot hole: As shown when Robin comes under the influence of Slade's mind control device, the hypnotized people retain their abilities and higher intelligence, just with a loyalty to Slade. That being said, when Slade hypnotizes all the DC heroes, Superman and The Flash are among them in the theater. Slade orders all the heroes to chase after and destroy the Teen Titans. The Titans take off on foot with the others running after them and are able to keep their distance in a big chase sequence. Superman and The Flash never use their super speed to over take the Titans, which would have been so very easy.
Revealing mistake: After Robin starts to believe that the Teen Titans are in fact a joke, he gets sad and goes out a hole in the wall saying goodbye to them. He fires his grappling gun up and steps out of the wall. But his arm remains bent as he stands casually in the air to be taken upwards. There is no effect of gravity or any realistic body motion in those moment. As his weight should have had him dangle down with his arm stretched out above him and him swaying like a pendulum. Instead he appears as a stationary action figure in a single pose with his elbow bent as he's taken up.