Batman put a spy-satellite in orbit that contributed to the deaths of thousands of people, the unlawful kidnapping of many others, and of course the near-destruction of earth.
He came up with plans to kill the Justice League that he left where a villain could get to them, and then he was too distracted tracking down his mommy and daddy's corpses to help any of his allies.
Nightwing joined the mob as a petty enforcer, worked for Deathstroke, and pissed him off enough to get a city irradiated.
Bab's screw ups have been detailed above.
Cass went psycho killer. Twice.
I think Stephanie's pretty representative of their symbol, actually.