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.
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.
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.
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.
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