Plot hole: Lee and Dawn overstay their tourist visa in the US, then fly back to the UK for the Office Christmas party. They then get into a taxi to go out to the airport in order to return to the US. They're kidding themselves. As I know (to my cost) when you overstay a tourist visa, the US Immigration Service finds out when you check in at the airport on departure. They'll be refused reentry, and probably barred from entering the US for up to six years. (I got a three year ban.) Neither Lee nor Dawn could possibly be unaware of this nor think they could beat the system as they would have been arrested when they checked in in Florida on departure (as I was), and they would have remained in small holding cells until the paperwork banning their return had been processed and their passports stamped 'Invalid for U.S. Entry', as mine was. (All this takes about seventy two hours, so they'd have missed the Christmas party anyway.) The mistake is NOT that they were able to leave the USA - that is explained (it's still not possible, but in the context of the show and the suspension of disbelief we are meant to believe it) the mistake is that they are on the way back to the airport to return. That's absurd. They would have been under no illusions as to their banned status re reentry to the USA.
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.
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: Season 5, episode 20 (My Lunch). One of Dr. Cox' patients needs a heart valve transplanted. Heart valves don't have to be transplanted from another person. They can be replaced by a metal valve, or the surgeon can create a new valve from a different part of the patient's body. There was no reason to wait for a donor valve when they had other options available.
Plot hole: In the start of season 4 we meet Liberty's little brother, Danny. J.T. and Manny are making fun of him because he is new to the school and is starting out. If he is starting out, then he should be in the 7th grade, because it is stated in the first episode that the school changed into a 7-12. Liberty, J.T., Manny, Emma,Toby etc. are all in the 10th grade so how does it end up that Danny is a grade below Liberty?
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)
Plot hole: When Lizzie and Gordo are sitting at lunch, Gordo says that he doesn't like broccoli (referring to the pile on his plate) and that he tries to avoid it. However it is established in many scenes that Lizzie's school has a self serve cafeteria, so why does he have broccoli? (00:56:45)