Plot hole: The (real) villain of the episode needs for their own agenda to retrieve the knife Kate brought to the Crows' headquarter in hopes to have it analyzed, and they assault Kate and Sophie while they are in the garage discussing the matter. Even assuming that the villains knew the two women were in that particular location having infiltrated security at the Crows (at the end of the episode Christine speaks of 'whatever surveillance was in the garage', not exactly sounding like she knows any detail), they had no way to know they would be there at all. They were in the garage just because Kate asked Sophie for 'somewhere private'. If their goal was to prevent Kate from having the knife tested, they needed to stop her before she got to the Crows at all. (00:12:20)
Plot hole: Batwoman sees live on TV the explosion that sends the truck into the river, while she is in the clinic of her stepsister on top of a building. She needs to go get her bike and drive to site. Fox says that she is "5 minutes out" when the truck is shown going completely underwater, with Alice inside who has been unconscious all the time. Even assuming that she makes it in less time than that, she still has to leave her bike somewhere and access the river from a somewhat secluded spot and swim to the spot, because the bridge is crawling with cops. There is no way that Batwoman would be able to save her and Alice would be totally fine, needing simply an aqualung to get back to her senses (and somehow survive an explosion that nearly kills Batwoman with her padded 10 million dollars suit).
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.
Who Are You? - S1-E4
Plot hole: Analyzing the remains of the explosion on the bridge does not lead to the retrieval and identification of the detonator who triggered the bomb, but Sophie deduces that it must be unreleased technology from Hamilton's, because of the extreme precision with a convoy that had 7 vehicles. The vehicles in the bridge scene in episode 2 were proceeding in a line and several meters apart. There was nothing unique in the detonation as shown, any stooge pushing a button on a remote control could have hit with the same 'precision' without breaking a sweat. (00:12:30)
Who Are You? - S1-E4
Plot hole: Fox is alerted by the alarms that there is an intruder in the house, exactly in Wayne's office. He has to make his way up from the Batcave to the main residence, enter by the door and then he gets knocked out by Magpie. As it turns out at the end of the episode, she had the place perfectly scouted (and it was shown anyway that the intruder was already in the office when the alarm rang), so there's no reason at all why she'd still be there to assault him, considering the necklace was not guarded by some bulletproof crystal or anything of the sort and if she planned such a bold theft in broad daylight she surely wouldn't take her time to get what she came for. (00:15:25)
Who Are You? - S1-E4
Plot hole: The whole "booby trapped frozen room" does not make any sense. Let's try to ignore the fact that it is entire speculation and a huge leap of faith on Mr. Fox's part that the trap works that way or that it's the only one, and that it wouldn't make sense (especially for a thief) to have something so erratic rigged to destroy your whole expensive equipment and jewelry stash - at most something directed at the door or a small charge to destroy your HD to cover your tracks. Still, it is supposed to react to any minuscule variation of temperature in the room and is triggered by a small sneeze, but Batwoman opens the door normally, and that alone would create a variation in temperature much bigger than her breath's (just think of what happens when someone does that in real life!). (00:21:40)
Who Are You? - S1-E4
Plot hole: The whole pearl necklace situation is a scene choke-full of mistakes. What we witness is Batwoman 'protecting' people from explosions of terrible superimposed CGI who look absolutely harmless, don't hurt anybody, are generally tiny and at great distance from everyone. The culmination happens when to thwart the threat of the single pearl left (the pearls all explode at different times, must have super high tech nano-detonators) Batwoman throws the batarang with millimetre precision at the small hand of a little girl, somehow knocking away the object, somehow not making it explode (how could she know hitting it violently wouldn't?) and leaps on the girl to shield her eyes from the explosion. Explosion which should be very distant since it comes from a single tiny pearl violently knocked away by a metal batarang before Kate' sprint, but somehow is still so big and devastating to horrify the crowd, larger than anything seen in the museum with dozens more and close by.