Factual error: Alice and Kate's little reunion underwater is disrupted by policemen that fire at them, and one of the shots reaches the transport truck, ignites it and makes it explode. The scene is baffling; forgetting the complete disregard for fellow policemen in the vehicle, how would bullets have enough strength to penetrate into an armored truck deep underwater, reach a critical weak point from that angle (the truck is upright, they should be barely get to shoot the roof of it) and still underwater cause inside the completely immersed vehicle a spark that would ignite fuel and make the whole truck explode? (00:31:45)
Factual error: Kate fires a grappling hook into the back of the runaway train - it punctures the thin back door easily. She then fires another one backwards which hooks against one of the sleepers on the tracks. The slack gets taken up...and the train jolts to a dead stop as the hooks bite, (with everyone just wobbling on their feet somehow). No way on earth that's possible - the back door would have been torn off/open like a tin can and/or the sleeper would have been yanked out out of the ground, and the train would have ploughed into the station at full speed. Not to mention the fact that only after the train stops does the sleeper apparently give up the ghost and break. The magical supermetal of the train door is somehow still intact.
Continuity mistake: In her rooftop fight with Tommy, Batwoman opens with a batarang, then sends him face down kicking him from behind. They wrestle some, and the railgun goes off once. In a wide shot when she punches him in the midsection a few times while he is trapped in an armlock, you can see the gun on the ground. He had it in hand in the previous shot and is still in his possession later. (00:35:00)
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.
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)
Factual error: The villain drops the elevator full of waiters and catering staff; the display gives him no indication of whoever is in each elevator, but we can maybe assume it was a staff-only elevator and he knew it (it surely had no markings to indicate it). When Kate reaches the ground floor, everyone inside that elevator is lying unconscious in the corridor. I could understand if the survivors crawled there, but everyone is simply KO meters away from the elevator as if the impact happened there and not in the elevator shaft with a devastating buildup that had to be vertical and contained for obvious reasons. (00:29:30)
Character mistake: Batwoman does everything she can to rescue the elevator falling down after the villain detonates the bomb, but does nothing for the second one Tommy blows up to make her lose her footing when she is vulnerable. There is no message from Luke telling her anything, and she is not shown having a HUD with thermal readings or something like that, so there is simply no reason why she would risk everything to stop one elevator and completely ignore the fate of the next one which could be full of civilians as well.
Factual error: The villain triggers the detonation that causes the elevator with Kate's dad and stepmom to start falling. After an initial hiccup, the cabin begins a freefall. Only after this real fall begins and the elevator already fell a few floors down, Batwoman lands on another elevator. Pauses. Shoots her rope to the top of the shaft. Hooks it. Pauses. Shoots from Chekhov's gun the double edged harpoon, which effortlessly sticks to the top of the elevator cabin and halts the ruinous fall with a smooth slowdown and no oscillation. All of that happening because somehow the elevator in all those seconds is just a handful of floors lower, even if it was plummeting at breakneck speed from the very first shot. (00:35:40)
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)
Continuity mistake: In the lobby, Mary advances towards an injured woman she diagnoses from meters away. Seen from the front, she is holding her phone in the right hand. In the back view though, she has it in her left hand. The phone switches hand again when she commands the paramedics to go check her again. (00:32:45)
Revealing mistake: Batwoman gets shot in the alley; the bullets create bad looking CGI sparks each time they hit her suit. When she gets back to the cave and sits down as Luke scolds her, you can see her suit bends and folds at the breastplate all rubber-like, making even more unlikely the fact that bullets would create sparks on impact (for what is worth, in the following episode there's a close-up of a bullet hitting the breastplate of the suit and there is no trace of sparks and not the slightest give from the material). (00:02:00 - 00:03:55)
Factual error: The very first shot of Kate and Reagan taking a walk in downtown Gotham for the lunch date is a wide-angle view. Several flags on the right side of the screen are visible, including the City of Chicago flag with its 4 red stars and the State of Illinois flag. (00:13:20)
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)
Continuity mistake: Tommy makes his unceremonious exit, and Kate spots Reagan. During the sequence with her, the same couple (she wears a reddish dress and has black hair in a ponytail) appears by the stretcher and then a few meters behind, even further behind when the camera is on Sophie reacting to her "There you are." (00:39:10)
Continuity mistake: After the title screen, Sophie is reviewing Batwoman footage. First shot and two agents, one with a hat and one with blonde hair in a bun, walk behind her, right to left, met by another agent looking at something in her hands. Cut to the screen Sophie is looking at, and a few seconds later the same extras are doing their exact same walking routine starting from the exact spot. (00:01:25)
Continuity mistake: In Bruce's office, the museum curator turns around to ask her assistant "Margot, is that the last lens change?" She initiates that line holding the handbag with her right hand, but in the reverse shot she is using that hand to point at her, since the purse instantly went under an armpit. (00:04:10)
Continuity mistake: In the three-way meeting during the museum party, Sophie says "Sorry, I didn't realise you were here with anyone." A woman in a flower dress passes right behind her. Cut to Kate for awkward moments of silence, and back to Sophie, with the woman who did not make a millimeter of progress in her walk during that second. Even worse, seconds later when she says "You two have fun" the same woman is repeating the action from the beginning. (00:28:25)
Continuity mistake: In the orphanage fight, Kate at one point is pushed against a pillar by a villain who holds her against it. She grabs a fire extinguisher and smashes another guy in the jaw with it. She does not drop this weapon nor hits with it the villain who is holding her, but in the next shot she is just punching and elbowing him. (00:19:05)
Continuity mistake: In the elevator, Kate's dad is looking at the electric wires with a flashlight. His wife says "How can this city trust us to protect it", and he lowers the torch. Next shot, he has it still pointed at the circuitry, and he lowers it only a second later. (00:31:20)