Other mistake: Kara never has enough room to wear the super suit beneath her clothes.
The Adventures of Supergirl - S2-E1
Continuity mistake: When Kara saves the chopper the sun on the floor changes between shots.
Continuity mistake: When Vartox starts to fight Kara the sun changes between shots.
Continuity mistake: When Vartox attacks Kara from behind the background changes in the next shot.
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