Plot hole: Dr. Adam Soong is initially presented as a discredited scientist, banned from the scientific community; he gets debarred and his funding revoked. And it's not an internal matter; he is publicly exposed for it. His daughter in episode 6 even finds out this information on Google. Several news articles call him "mad scientist" and such. However, this same person at the same time throughout the rest of the season has every bit of pull and influence, not just through undercover channels, but is treated with the utmost honor and deference by the NASA PR people at public events.
Triumvirate of Terror! - S3-E8
Plot hole: After Superman thwarts Lex's plan and knocks the Kryptonite into the sewers, Lex yells in frustration, splits his power suit off and flies away on a jet pack. Superman just lets him go. Wouldn't Superman chase him and catch him, especially seeing as how weak Lex would be like that? (00:07:35)
Plot hole: The demented villain is not keeping tabs on the elevators! The rescue teams can move freely around the tower, the elevator doors can be pried open with ease like Sophie and her husband do, so his threat is completely empty and ineffective, somewhat surpassed in idiocy only by Batwoman's response, who during the ultimatum gets back home and keeps busy spraypanting the suit and finding a wig for her date with the crazy guy at the top of the hour rather than taking 10 minutes or so to free the people trapped in the 7 elevators first, unopposed as she is, and go challenge the idiot later when he has no more hostages. It shoud also be noted that the villain made the "hostage" situation and the "one hour" ultimatum known only to Kate! The police and the Crows have no reason at all not to intervene with full force to check out who the crazy bomber guy is, but the police does not swarm the building and nobody finds odd to see a madman on top of the building under terrorist attack.
Plot hole: When Frankie tries to get Johnny to chase her out into space, he tells her he can't follow and warns her to turn back due to the thin atmosphere not being able to keep their flame powers active, and indeed her flames die out, and she begins falling back to Earth. However, several minutes later in the episode, both of them are just outside of the Earth when Terrax arrives, and again at the end after she becomes the new herald of Galactus, Johnny follows her into space well beyond Earth before his flames die out. (00:03:15 - 00:06:03)
Plot hole: White Base and the interior of Luna II withstand without a scratch the explosion of the thermonuclear reactor from the Magellan from just a few meters, while the blast literally vaporizes the Zaku far away from the entrance and threatens to damage the Musai, hundreds of meters away.
Plot hole: Lucien, Trustan and Aurora are somehow compelled to believe they are Mikaelsons, when no-one knew how to compel until Elijah compelled Aurora by mistake when they fled. So when did this supposed compelling happen? Did Elijah go back and do it later on? The siblings all had knowledge of him compelling them, so I'm confused exactly when they all learned of their ability.
'Unmei no sentaku' mitaina - S1-E6
Plot hole: Akito's attack is point blank, on a ship part of a fleet with Distortion Field activated (basically, they have shields, like the good guys' robots). The explosion he causes is according to Ruri's damage report big enough that it managed to vaporize 80% of the ships they were facing, but his Aestivalis and the other 3 right floating nearby make out of it literally without a scratch. (00:05:10)
Plot hole: Owen is unable to give Henry the kiss of life as he has no breath, and yet he is able to talk.
Left Behind - S1-E9
Plot hole: It's revealed that Chronos is Mick from the future after he was abandoned by Snart. However, in the episode White Knights (episode 4) the earlier version was able to sneak up on Chronos and surprise him with an attack from behind. If that was a future version of Mick then surely he would have remembered the attack coming and could not have been so easily caught off guard.
Plot hole: In the lab when Liz makes the slides of her cheek cells and the cells from Max's pencil, the first time she doesn't add stain and the second time she does. If she's going to be a molecular biologist she really ought to learn to apply techniques consistently. (00:07:30)
Plot hole: The grounder's leader Anya states that the missiles (flares) burned a village to the ground. If this were true, the flares couldn't have flown very far, otherwise that village would have been too far away for the grounders to know about. In a previous episode, when you saw the flares from space, it was obvious the flares traveled hundreds if not thousands of miles away. (00:31:30)
Plot hole: In the end of the episode, Wolverine is seen recuperating after surgery removes the microchip in his brain, and his head is bandaged. Performing invasive surgery on Wolverine's brain isn't possible, since that would require going through his adamantium-infused skull and no conventional material is capable of that. Only a less invasive technique (such as going through the cranial sutres or cranial foramen) would have been effective and that most likely would not have required Wolverine's head to be bandaged (especially with his rapid healing mutant ability).
Over My Head - S3-E4
Plot hole: Daphne was able to hurt Duke because his name appears on her cell when he called, but names only show up on a cell phone if the person's number and name are programed into the phone, and Duke has already said he doesn't know her.
The Monsters are Due on Maple Street - S1-E22
Plot hole: The street sign in the beginning is all wrong: it faces the camera rather than the street where the story takes place. In a typical American city, street signs are almost always placed in the direction of the street they are indicating, so drivers on the other street in the intersection know what they are turning onto or passing. In other words, the story is not set on Maple Street! Maple Street is the intersecting street at the end of the road the story is set on.
The Messiah on Mott Street - S2-E38
Plot hole: No one in Goldman's house finds it at all strange that a mailman arrives at the door with a letter after midnight on Christmas Eve. Nor, a short time later, does the doctor or anyone else passing by at this very odd hour wonder why the same mailman is collecting mail from a street box at dawn on Christmas Day.
Plot hole: In the hoverdrone footage, Peter goes down suddenly during the gunfight, apparently from a wound to either the head or torso. However, there is no wound or blood on him and even his bulletproof vest has no marks except for the normal studs. If he had been hit in an extremity he would not have limply collapsed instantly. Sonrisa's goons are using automatic weapons that should have no trouble hitting him many times from that range of only a few meters. (00:54:00)
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.
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.
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?
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.