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.
Father Time! / Apartnership! - S1-E4
Plot hole: Timmy uses his heat vision, that he previously wished for, to win the race for his future dad. But it's revealed later in "Smarty Pants" that if you use a previous wish in a contest, it is magically taken away because it's cheating.
Suggested correction: That is true, that rule was mentioned in a later episode. However in the episode Christmas Every Day, it was revealed that new rules could be added at anytime. So it's possible that the rule simply didn't exist yet. Although, this plot hole may apply to any episode released after "Smarty Pants."