Plot hole: This is another movie where the cops are too dumb to go out by themselves. The woman who icepicks the first victim (we see) to death would have left enough forensic evidence on the scene to convict her ten times over - skin, hair, sweat, saliva, vaginal fluid, possibly blood, and they all contain DNA in abundance. She had vigorous, sweaty sex with this man and she didn't clean up afterwards (and she couldn't have done so thoroughly enough anyway) so she's left calling cards all over the place. The killer also handled the icepick (which the police take away in an evidence bag) with bare hands - her prints would be all over it. She might as well have left a signed confession, but they can't even identify her. Sharon Stone, for instance, leaves her fingerprints (on the chair and fixtures in the police station) and her saliva (containing epithelial skin cells which are an excellent source of DNA) on the cigarette butt she discards, also in the police station. She went there of her own accord and these artifacts are legally accessible by the police. It is obvious to anyone that the women who had sex with the victim killed him, and Catherine is most certainly a suspect. They don't have enough to charge her but they would if they did a simple series of tests on the dead man's body - and if she didn't do it, that would eliminate her as a suspect. They don't even check.
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: One alien egg is shown hanging from the wall at the start of this film, yet there's no way it can be there. The queen didn't take any with her from LV426 in 'Aliens', and if she did, she had no opportunity to place them on the Sulaco between exiting the dropship's landing gear, engaging Ripley and being killed.
Plot hole: There's no way Dr. Lynn Waldheim's coat would have fitted Carter.
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: The rule is Each buries his own as stated in the first movie. So Gus wouldn't have came back to life because he was buried by Drew and Jeff.
Plot hole: How is it that the Flying Elvis' have an extra parachute on board for Jack?
Plot hole: The cops are waiting for the robbers to arrive at the hideout after the robbery so they can bust Joe, and most certainly, they would have put surveillance on the warehouse. So why don't they intervene when Mr. Orange is presumably seen wounded outside of the hideout, or especially when a kidnapped cop is brought inside the warehouse? Cops aren't going to waste any time whatsoever letting one of their own be put in mortal danger, even over serious business.