Plot hole: When the two henchmen who break into Nick's loft to kill Lisa are captured, the case is closed. But the two thugs were reporting back to a boss who wasn't caught, and who surely would have sent more hitmen after Lisa. So the case shouldn't have been closed.
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)
The Tale of the Mystical Mirror - S5-E3
Plot hole: It makes no sense that Ms. Valenti gives all of her employees a compact mirror and also invites them to her home. Any of them could open their mirror while standing near a painting of Ms. Valenti and they would discover the secret, as Cindy does.
Suggested correction: The compact mirror includes a palette of cosmetics. Cindy shows it to Laurel, who says, "She gave one to me, too, like we're ever gonna use it." Presumably, the employees are mostly using the free samples of cosmetics from the shop displays. I myself have owned some compacts that I didn't always want in my purse (if they were too big or awkward in a certain purse).