Shelter from the Storm - S3-E18
Continuity mistake: When Winn and Brainy hug, Winn starts the hug with one arm high and one lower, towards Brainy's waist. The shot cuts and both his arms are up and in the centre of his body.
In Search of Lost Time - S3-E15
Continuity mistake: When Samantha sees the surveillance video of her transformation into Reign, which was triggered by Lena provoking her, their dialogue is slightly, but very distinctly, different than it was a few minutes earlier. (00:20:15 - 00:25:25)
For the Girl Who Has Everything - S1-E13
Other mistake: In Kara's hallucinations of Krypton, the planet is shown with a yellow sun. Rao, the supergiant around which Krypton orbited, was red.
Continuity mistake: As Kenny is about to sit down opposite to Kara, the juice on his tray is lying down on it. Next shot it is standing up.
Homecoming - S2-E14
Continuity mistake: In the scene at the end where Mon-El goes to Kara's to try and console her, right after he sits down and she shifts to lean on him the blanket falls off her shoulder, but in the next shot it's covering her once again. (00:40:35)
Continuity mistake: Mike and Kara are in the alien bar in the both talking about Mike not controlling his powers. When Mike breaks the glass there is no other glass on the table. In the next shot a glass appears at the edge of the table, in the next shot the glass is gone again. (00:03:30)
Continuity mistake: When J'onn J'onzz is fighting Miss Martian in the ring, she punches him into a wall, leaving a massive dent. She missed the next punch, and the plaster on the right hand side of the dent falls out, but the plaster on the left is fine. Miss Martian then throws J'onn across the room, and in the background, the dent is visible, but it is now the left hand side of the dent where the plastering is missing and the plastering on the right is now mostly in place.
Continuity mistake: The bottom circle on the left drawn by Barry on the whiteboard changes shape between shots.
Continuity mistake: While Kara is on the ground after livewire hits her with electricity, the sun changes between shots.
Continuity mistake: While Kara and Alex are on the beach the sun on the floor changes between shots.
Visible crew/equipment: When Winn is putting on his shirt after being caught, you can see his mic wire through the hole where Kara says he forgot to button his shirt. (00:03:15)
Continuity mistake: While Kara is fighting Reactron at the junk yard the sun on the floor keeps changing.
Continuity mistake: Before Kara uses her heat vision against Vartox she gets some dust on her suit, then she stands up and the dust is gone.
Continuity mistake: When Cat is on the talk show, the microphone on her collar keeps disappearing and reappearing between shots.
Continuity mistake: When Alex brings donuts to try to convince Kara to come back to the D.E.O., Kara picks up 2 donuts which suddenly change to 1 once she sits down, and then back to 2 a few shots later in a wide shot.
Other mistake: Supergirl walks into the gallery returning the painting, says "di nada", then takes off straight upwards...presumably blasting her way through the ceiling.
Character mistake: When Kara breaks her arm, she says that she doesn't need to go to a hospital because the bone will heal when her powers return. She would still need a splint or a cast to ensure that the bone sets in place properly; leaving it untreated runs the risk of a physical deformity or other unforeseen complications down the road.
Other mistake: During the boardroom meeting with Lena, James, and Morgan Edge, Katie McGrath's natural Irish accent briefly, but noticeably, slips out.
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.
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