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.
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)
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.
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