Continuity mistake: As they are fleeing the alien base, Supergirl and the others run towards the portal, Winn activates it and jumps through. In a following shot (after a 'friendly' alien helps them), he is standing behind Supergirl again. (00:32:00 - 00:32:35)
Other mistake: During an argument, Maggie's father mentions the border wall being built to keep people from entering the country illegally. This is obviously a reference to the real-life presidency of Donald Trump, but within the show's continuity, his comment doesn't make sense: in "Resist", the penultimate episode of season two, it's revealed that President Olivia Marsdin is literally an alien from outer space, and earlier in the season in "Welcome to Earth", she signed an executive order offering aliens such as herself full citizenship if they so desired it. If she's that tolerant of extraterrestrials, it seems unlikely that she'd be so intolerant of foreign immigrants as to resort to such an extreme action in foreign policy like building a wall on the border.
Continuity mistake: Rick Malverne has handcuffs on when J'onn goes in as his dad. When he figures out it was J'onn, he tells them they have "23 hours and 14 minutes," looks at his watch and the cuffs are gone. (00:21:30 - 00:25:00)
Crisis on Infinite Earths: Part One - S5-E9
Continuity mistake: Oliver still has a quiver full of arrows when he's making his stand at the end. A shadow demon knocks him down and all of the arrows disappear instantly. They've not been knocked out of the quiver onto the ground, they've disappeared entirely.
O Brother, Where Art Thou? - S4-E15
Character mistake: During the opening scene, while Lex is talking to Lena he says he was quoting Epicurus from 230 years prior. Epicurus died in 270BC, making that quote around 2300 years old.
Character mistake: President Marsdin says that Camp David was named by President Eisenhower in honor of his son and grandson. It was actually named for his father and his grandson; his sons were named John and Doud.
Continuity mistake: Right after Alex is freed from the water tank, in the shots of Maggie holding her, Alex's clothes are bone dry.
Factual error: The Marine Colonel in Supergirl played by Eddie McClintock spends all of his time wearing Marine Officer's Dress Blue Bravos. Marine Dress Blues are ceremonial uniforms. On rare occasions, the Charlies or Deltas (no coat) may be worn as a work uniforms (the primary exception to this rareness being recruiters). The full uniform is certainly not worn for day to day work in the field.
Continuity mistake: Livewire has part of her hair over the front of her right shoulder. A shot later after discovering her powers suddenly her hair's over the front of both shoulders.
Continuity mistake: Kara and William review the article William has written about hate crimes against the transgender community. The article text is shown, and it states that Yvette's attacker, Gregory Bauer, was arrested. But Gregory is not identified and arrested until Dreamer confronts him that night.
Continuity mistake: Maggie comes to Alex's apartment with pizza. When Alex opens and closes the pizza box, she folds the pizza box edges in and 3 shots later the edges are outside of the box.
Factual error: After his father escapes from prison, Winn is interviewed by the FBI. Escaped fugitives fall under the jurisdiction of the Marshals' Service.
Continuity mistake: During the fight between Supergirl and her clone, the clone blasts Supergirl with her purple lightning power, which causes a small explosion and also somehow turns the sky from bright dusk to nighttime.
O Brother, Where Art Thou? - S4-E15
Factual error: While the location of National City is never revealed, it is generally accepted that it is located in the US. But all the helicopters used to fly Lex around are Canadian.
Other mistake: J'onn J'onzz starts a private Investigation company. He is shown looking at the new PI license he just placed on the wall. But the certificate says it is a renewal. (00:05:30)
In Search of Lost Time - S3-E15
Revealing mistake: During the mental block Alex stops the fight between Winn and the Asian guard then she hits him twice. The punch to his face misses by inches but he falls anyway.
Continuity mistake: The sketch that Brainy shows to Winn is meant to be his original sketch that he drew in the previous episode, hence why Winn is so shocked he's somehow got it. But it's slightly different from what we actually saw him draw at the time.
Continuity mistake: The shield design that Winn sketches on the paper changes between him starting to draw, and him showing it to his friend a second later.
Not Kansas - S3-E21
Revealing mistake: As the guy fires the machine gun at Guardian, there's a closeup of bullet casings falling to the ground, but they're not just empty casings, they're fired blank rounds.
Answer: For one, it's usually cheaper to film in Vancouver because of the tax breaks. But all the CW Arrowverse shows (with the exception of "Black Lighting") are/were filmed in Vancouver. So it makes it easier and cheaper for sharing set designs, crossovers, etc ("Black Lightning" filmed in Vancouver during its crossover). Originally "Supergirl" wasn't part of the Arrowverse when it was on CBS, but it was too expensive to produce and wasn't reaching the wider audience the CW shows had. So CBS moved it to its sister company, The CW.
Bishop73