Plot hole: Batman finds at Belson's home a handwritten list of substances needed for a transplant. Why would Belson, a medical authority in the field that knows those things thoroughly, even write a list down? If it's for Freeze to procure him the material, why would it be at his house and not with him, and when did he even have time to be at home to do that, since he has been kidnapped by Freeze when he was driving on the outskirts of Gotham and taken to the oil rig? If he had time to go home, he at least would have changed clothes, he's still in the tuxedo he wore when he was kidnapped the night before.
Continuity mistake: Sandra and her strong man are pursuing Jack and Bridget. They almost catch up to them and bang up both sides of their wagon in the car chase. Bridget and Jack escape, with eventually Sandra and company in pursuit a way behind them, tracking them on an alien computer. When they reach the power plant where Jack and Bridget are, their car has no damage at all. (01:18:20 - 01:29:05)
Other mistake: In the scene where Vir gets in a fight with Zack you can for a moment see the Rolex that Stephen Furst is wearing on his right arm. (01:21:10 - 01:21:20)