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.
Day 2: 7:00 A.M.-8:00 A.M. - S2-E24
Plot hole: Peter Kingsley is shot and killed by a man in a helicopter just as he is about to kill Jack. Kingsley would definitely have heard the helicopter approaching.
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.