Plot hole: During the investigation for the security breach at Wayne Enterprises, the policemen are recalled for an emergency at the Gazette. (would make no sense that they are so short on men right in the core of the city that they'd need to call people away from an active investigation like that, but fine). The radio code used is "10-54", which is supposedly according to sources online "possible dead body", it perfectly fits the situation. When Kate arrives on site, people are just then starting to flock the area. Where have they all been before? It is impossible that someone called the police on it, who are somewhere else entirely, but several minutes passed by and every curious bystander is just arriving now with the protagonist. (00:11:50)
Plot hole: Kate in the Batcave says with absolute certainty "Alice doesn't know that Bruce Wayne is Batman. Whoever stole the gun, knew that Bruce had to have the suit to test it on." Both statements are leaps in logic with no foundation. Alice knows that Kate is Batwoman, and that Bruce's office is her center of operation (she even shines a bat-signal there!). It would be perfectly logical to assume that she made the connection. The testing bit is simply a non-sequitur; plenty of weapons can be made and tested on armor which fits the specifications, real or inferred, of a particular target, without being in possession of the item as a whole. (00:16:00)
Plot hole: The demented villain is not keeping tabs on the elevators! The rescue teams can move freely around the tower, the elevator doors can be pried open with ease like Sophie and her husband do, so his threat is completely empty and ineffective, somewhat surpassed in idiocy only by Batwoman's response, who during the ultimatum gets back home and keeps busy spraypanting the suit and finding a wig for her date with the crazy guy at the top of the hour rather than taking 10 minutes or so to free the people trapped in the 7 elevators first, unopposed as she is, and go challenge the idiot later when he has no more hostages. It shoud also be noted that the villain made the "hostage" situation and the "one hour" ultimatum known only to Kate! The police and the Crows have no reason at all not to intervene with full force to check out who the crazy bomber guy is, but the police does not swarm the building and nobody finds odd to see a madman on top of the building under terrorist attack.