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: In episode 4-16: "Lucy," there is no reason for the criminals to be chasing Lucy on the ski slopes at the beginning of the episode. We learn later that she's been working with them all along; she calls Lois during the chase, and the call is part of Lucy's plan with the criminals. Lucy being chased by the criminals would make sense given the story she gives Clark during the next part of the episode, but it doesn't make sense for what we ultimately learn is the truth. And nobody from Smallville is anywhere near the ski chase, so it also doesn't make sense as any kind of a ruse.
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)