Plot hole: Pike says he doesn't want women on his bridge, Number One being the one and only exception, and he keeps ordering Colt off it. His apology to Number One indicates that A) he doesn't think of her as female, and B) she's the only exception to his rule. So how does he overlook the very female crew-woman seated at the science station? (00:06:55)
Plot hole: After stressing (as Waverly did earlier) that only a laser beam can activate the explosive crystals, LeGallows demonstrates the destructive power of one - using only sunlight. (00:37:15)
Enter Batgirl, Exit Penguin - S3-E1
Plot hole: When he abducts Alfred, believing him to be a minister, Penguin suffers a peculiar memory lapse. He's encountered Alfred twice before in previous episodes, even kidnapped him once before (knowing full well that he was Bruce Wayne's butler). Yet here, he fails to recognize Alfred at all. (00:12:30)