Continuity mistake: In the bistro, Batman thwarts Joker's booby-trapped juke box by whipping out his bat shield. Afterward, he places the shield on the floor behind him. In the next shot, as he turns around, the shield has disappeared. He and Robin race off without retrieving it.
Continuity mistake: When Batman surprises Joker and his henchmen in the gym, his shadow is on the wall behind them, his cape spread out and forming a menacing bat shape. But when the shot cuts to him and Robin, Batman's cape isn't spread. He's standing with his arms down.