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.
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