Plot hole: Hippolyta tells Hawkgirl of Aresia's background of being born in the outside world, the war in her country and right up to her drifting to the shores of Themyscira. It would be impossible for her to know anything of Aresia's background as in part two, it's explained that the captain of the ship who saved Aresia died shortly after reaching Themyscira and therefore would not have been able to tell Hippolyta anything.
Plot hole: Vaughan discovers Lauren is a mole when he goes through her briefcase and discovers the wig, gun and fake passport she used in Germany a few hours before - surely even the worst secret agent in the world would have enough sense to get rid of such incriminating evidence as soon as possible, and not carry it back to the USA (sneaking it onto a plane, presumably) and leaving it in the room where the man you're lying to sleeps. Lauren is a highly skilled agent, if the Covenant selected her for a mission this important, so it's out of character (without an explanation) for her to be so sloppy.
Plot hole: In 'Oasis,' several times in the episode, specifically when they took Trip captive, the holograms appeared out of nowhere brandishing weapons. The holograms can walk through walls, which we saw, but the guns were real. We saw them hit the deck when Liana deactivated the holograms. So how did they appear with the guns? (00:34:00)