Plot hole: After discovering the cards tossed into the ocean at the docks, Miss Dorothy goes to Jaden's dorm to alert him of this. There was no real reason for her to go to him, seeing as how she had no idea if this incident was tied to him specifically. (00:09:05)
Plot hole: Cadmus sets a brain-controlled Connor loose in public, without apparently remotely considering the possibility that anything might go wrong. When he regains control all they've got is a few goons onsite armed with regular ammunition - what did they think that would achieve? They know exactly what he's capable of. Either have kryptonite ammo or don't bother having anyone there at all.
The Spores - S2-E7
Plot hole: Hal and Roy could not open the spore case with an electric power drill, but later a married couple pops it open with a hammer and chisel, then much later some children acquire the case and easily open it.
Plot hole: When Nadia had been held captive in The Village, how did she get word to her accomplice to be ready at the exact time, in the exact location, and with a packing crate ready, and a whole series of transports arranged? Even if Nadia was in on the ruse of conning Number 6, wouldn't he be suspicious?
Recognition - S1-E17
Plot hole: Bridge could have used his powers to figure out if Wootox and Sky's bodies were still switched.
Plot hole: In Russia, Soldier Boy is shown heading to the airport, He wanted to get to the US and start his revenge against his team. Problem is: he has no documentation and money to take a flight. Even if he stole the money somewhere, still would be impossible to travel without the proper documents.
Plot hole: After Kara and Alex are run off the road, Kara is convinced by "Noel Neill", revealed later to be J'onn, to stop using her powers. From context, J'onn had to have been summoned by Eliza, but in 2007, she would still think he's just Hank Henshaw; she doesn't learn he's not, or even that he's a shapeshifter, until 2016, as seen in season 1's "Myriad", well after Kara and Alex have grown up.
The Feminum Mystique: Part 1 - S1-E5
Plot hole: If her younger sister Drusilla is sent from Paradise Island to retrieve Diana, how did she get to Washington DC or wherever, she had no way of knowing where her older sister would be.
Plot hole: This was the first episode of the series and we see that the rangers are unable to figure out how to properly operate their zords; but in Origins Part 1 (which takes place prior to this) they have no issues with the zords at all.
Plot hole: Skye's mother, Deborah, was held hostage by the Sixers for several years, though everyone believed she had died in an epidemic and was buried in Memorial Field. The Sixers kept her alive with medicine only they had to force Skye to act as their spy. Even though Terra Nova has a medical clinic staffed by doctors and nurses, it was never noticed that no one had witnessed Deborah dying, her body was never placed in the morgue, that was there no record of her being buried, or even questioned that there was no corpse. Deborah just disappeared without a trace and nobody wondered about it.
The Tale of the Mystical Mirror - S5-E3
Plot hole: It makes no sense that Ms. Valenti gives all of her employees a compact mirror and also invites them to her home. Any of them could open their mirror while standing near a painting of Ms. Valenti and they would discover the secret, as Cindy does.
Suggested correction: The compact mirror includes a palette of cosmetics. Cindy shows it to Laurel, who says, "She gave one to me, too, like we're ever gonna use it." Presumably, the employees are mostly using the free samples of cosmetics from the shop displays. I myself have owned some compacts that I didn't always want in my purse (if they were too big or awkward in a certain purse).
Plot hole: The nuclear explosion is on Liberty Island, a small yield, but nonetheless big enough to move an enormous amount of water towards the coasts on all sides. When we see Sertrakian and the others at the harbor no water is heading their way - they should be washed away by it. (00:37:30 - 00:38:45)
Plot hole: Dillon was quickly identified by the city sensors as having metal parts, thus classifying him as a threat to the city. Yet Tenaya, who is essentially a cyborg, tries out for the Green Ranger without setting off the same sensors.
Suggested correction: Tenaya wasn't caught because the guards assumed the equipment was faulty. It was giving positives all day because of all the sleeper agents we find out about later.
The Beacon - S1-E26
Plot hole: Barrows introduces himself as "Dr. Dennis Barrows," and Teddy asks, "What's a doctor?" As the isolated villagers have never heard of doctors, Teddy would have no way to know that "Doctor" was a title/profession and not simply part of Barrows' name. He should have asked, "What kind of a name is Doctor?"
Plot hole: The episode's climax concerns Bernie rushing to the airlock to stop the rest of the crew, who are infected, from flushing themselves into space. Except that he's infected too, so they can't flush without him anyway.
Plot hole: Sydney is able to surmise from the artwork (we could also say from the writing, but her rival is one step ahead of her for 2/3 of the episode and it is established that he does not know the language) the precise location of the koi in Lumbini. The map is 150 years old, but there's no way even with a big stretch of imagination to buy that they both'd be able to pinpoint with such ease and certainty its location in the basement of a random building in the bustling market center of a town, that surely changed plenty during the past century and that does not bear any special landmark.
Plot hole: Why would Danger Mouse go on the roller coaster at the end without seeing Greenback go on it first? Greenback went first in the ghost train. It also doesn't make sense that Danger Mouse would go on it when Penfold pretty much tells him flat out that it IS a trap.