Stupidity: The gun stolen by the villain was designed by Batman, according to Luke Fox, in case the wrong person got a hold of the batsuit, which is bulletproof. As shown in the previous episode, the suit has electronic devices like a defibrillator implanted inside, which are remote controlled (huge security hazards, but never mind) and has obvious weak points, like the jaw, that a skilled fighter like Batman himself could exploit. It is not an invincibility suit by any means. So Batman built a super-gun able to kill himself and stored it into a simple warehouse while having already a perfectly working prototype (so he basically keeps 2 of them around); he is obviously an idiot who built a devastating weapon that any villain can steal and use against him (or anyone with body armor and more) for no real reason, a weapon designed to kill and not disable, even, contradicting his MO judging by the rest of the arsenal.
Stupidity: Magpie in theory has the exploding pearls as diversion for her escape, but the pearls explode all too soon and in a room that she already emptied with the false alarm. Reality is that she has to face already zero security without the pearls being a factor, the moment she presses the alarm button. That's because for some reason every single Crow armed guard went to the exit to help the guests leave (in a most unprofessional way as they further crowd up the exit standing right in the way) and nobody remained behind to remotely keep an eye on the jewels. Also of course there is no alarm whatsoever on the jewelry cases, that can be opened at will. That is a serious joke of a security, and supposedly made by professionals, former navy seals, green berets etc.
Stupidity: The access to the Batcave is controlled by a mechanical lock with no security measure whatsoever. Not just that, but the butler guy even moves the key away putting it 3 inches away right next to the lock, making it all the more conspicuous because the lock this way is exposed and revealed as such! It even looks 'wrong' from a purely aesthetic point of view, nobody would have an odd hole in their shelf that makes the furniture look cheap and broken, it would be anyone's natural instinct to cover up something like that. (00:25:30)
Stupidity: Batwoman not only drives through town the same bike as Kate, in full Batwoman garb including the cape, but at the beginning of the episode is driving to Wayne enterprises, right inside the employees entrance (clearly marked as such). Even funnier considering the fact that the series keeps referencing things such as security cameras and people taking Batwoman pictures with their phones, elements that were not a concern decades ago and that would if anything require more caution, not less. The old Adam West show with all its camp and obvious absurdities had him at least drive his car to the outskirts of town and come in and out through a secret entrance, not his home garage. (00:03:00)