Plot hole: Delores is walking into the murder scene at the beginning of the movie just as Ernie is shot. Later, while she is being questioned, she tells the two detectives what the thugs said and did, yet, she was not eavesdropping or looking through the door.
Plot hole: When The Penguin is controlling the Batmobile, Batman punches through the floor to take off the transmitter. We still see a video feed of The Penguin. Why? Batman pulled off the transmitter, so there is no reason for there to still be a video feed.
Suggested correction: We see the Red Triangle gang spends a while fiddling with the Batmobile's workings before installing the transmitter. It's likely they made multiple 'modifications', thus the transmitter was for controlling the car's engine and steering, and the video feed was made possible by another, separate means.
Suggested correction: I concur with the other correction. There are multiple shots showing the gang working on the car and doing other things to it beyond just putting on the transmitter. (You see them playing with wires, moving parts around, etc.) Hacking into the computer/video-feed so Oswald could taunt Batman is likely among the other things they are doing. There's nothing into the movie that suggests taking off the transmitter should (or even could) interrupt the video-feed. The fact that Batman has to punch the screen to get rid of the Penguin's image is another point to the fact that the transmitter itself had nothing to do with the video feed.
Plot hole: The sheer distances Kevin covers on foot in one night are outrageous. Between 9pm and midnight he walks from Carnegie Hall to the children's hospital, to 95th street, back to the toy store carrying a large paint can and a large 2x4 (street signs here put it around 59th and 5th), back up to 95th, then all the way back to midtown, to Rockefeller Plaza. One way from W 95th street to around E 59th and 5th Ave. is at least an hour on foot for an adult, he does this 4 times between 9pm and midnight, once while carrying a 2x4 and paint can, once while being chased by 2 adults, and he still has time to set up a house full of traps.
Plot hole: When Rane and the other terrorists come out the bottom of the plane and start walking towards the fairgrounds, it is amazing how not one police officer or staff member of the airport notices that they came out from under the plane, or that they don't seem to be walking off the plane like the other passengers.
Plot hole: While we never see Lisa leave the courtroom at the end to call Judge Malloy to send the fax verifying Jerry Callo, it is possible she snuck away for a minute to do it after the dismissal and before they leave the town. However, Vinnie does not ever seem to mention that he told the judge he is Callo to her so how did she know? He must have mentioned it to her while they were rushing to leave, they were back on speaking terms and she called Malloy.