Plot hole: When Two-Face and his men have broken into the new D.A.'s office to find dirt on Rupert Thorne, one of his men finds a file detailing Thorne's record of Swiss bank accounts, money laundering, blackmail and payoffs that Two-Face tried for years to subpoena when he was D.A. When Thorne finds out that Two-Face has the file, he states that he will be ruined if Two-Face gives the file to the police. If Two-Face tried unsuccessfully for years to subpoena the file, then in all likelihood that means Thorne paid off the right people to prevent the subpoena from happening, so Two-Face giving the file to the police shouldn't be a problem for him. Additionally, if giving the file to the police would be all that it would take to bring Thorne down, then the new D.A. could have already done so. If the new D.A. was also paid off by Thorne, then it wouldn't make sense for Thorne to allow the D.A. to keep the file since they could easily lose the file or even double-cross Thorne. (00:10:45 - 00:14:20)
Plot hole: Alfred manages to find the bad guys because not only they grabbed the supposedly homeless guy off the street (Bruce in disguise), but also somehow brought his car to the scrapyard. If they knew it was his, they would have known something was off (a hobo with a car?) and they would have not got rid of it after more than a day. If they didn't, and they just towed out a random car, Alfred had extraordinary luck - nothing in fact would lead to believe that the truck was even related to the car.
Plot hole: The two agents split; the rookie goes down an alley, chasing the two henchmen, who reached their car and chase him back down the alley almost running him down. Batman saves him though, destroys the car and quickly interrogates a suspect. Somehow though he also manages to save Montoya, who went inside the warehouse right away as they split the warehouse. The timing does not work.
Plot hole: It's never explained: 1. How or who helped Scarecrow escape from his cell or 2. Why he'd be sitting in there at the end in costume instead of prison garb.
Suggested correction: Something not being explained is not a plot hole. The manner in which Scarecrow escaped his cell isn't essential to the plot, and therefore doesn't require an explanation. And the reason he's left in the cell in his costume is for the same reason Batman was left wearing his outfit when he was imprisoned: because the doctor at the asylum felt removing his outfit in his hallucinatory state could cause him to become catatonic.