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.