Continuity mistake: Kate arrives in front of the newspaper. Directly behind her a guy a bit on the chubby side is arriving as well. But he already was in the crowd shown before, looking at the dummy. (00:11:40)
Continuity mistake: In the shot when Luke puts back on the table the double action grapple hook, the large bullet-shaped item next to it changes position compared to the rest of the scene. (00:11:30)
Continuity mistake: The bat-signal (or bat-light as Alice calls it) is on a rooftop looking entirely different from the one established in the first episode (from minute 4 on). (00:03:10)
Suggested correction: Yes, because Kate re-designed it.
Ohhh, okay. I must have missed the part when she said she was doing it, my bad. Which episode?
I'll have to look that up, which I will when I have a chance, but it follows in line with the redesign of the batsuit and emblem.
Continuity mistake: When Alice quips "And I am the crazy one...!" at the sight of Batwoman's wig, her hand is on the breach, then suddenly between Kate's hands. (00:36:40)
Continuity mistake: In the Batcave, Kate holds the childhood picture with her sister by the sides in the first shot, by the bottom in the close-up. (00:08:40)
Continuity mistake: When Kate is writing the diary entry for Bruce, in the close-up the written part is taking barely half of the page, while in the overhead shot it is taking way more - the last lines being presumably actually scribbled by Ruby Rose have a much wider spacing. (00:40:20)
Continuity mistake: The hair on Sophie's cheek as she stares at Batwoman after landing on top of her and is in kissing range is parted in locks that move and differ across shots in noticeable way (for instance when Kate pulls the gag off her mouth there's a very thin one curling to her lips, but it's a thick lock right after). (00:35:00)
Continuity mistake: When Alice is talking to Jacob Kane with Sophie on the plank, she says "Can your little birdie fly?", holding the radio with all fingers straight and on the side of the device. Cut to "For if she moves an inch..." and her fingers are curled, with the pinkie at the bottom. (00:33:15)
Continuity mistake: The quantity of blood behind Batman's dummy changes; in the overhead shoot of the crowd it runs horizontally along the step for an area 3-4 inches wide, while in the subsequent close-up there's no such trim. (00:12:00)
Continuity mistake: In her diary entry at the end of the episode, Kate puts the pen down to fetch the file. She puts the pen by the diary at first, but in the next shot the pen is on it, in the middle of the page. (00:40:20)