O Brother, Where Art Thou? - S4-E15
Character mistake: During the opening scene, while Lex is talking to Lena he says he was quoting Epicurus from 230 years prior. Epicurus died in 270BC, making that quote around 2300 years old.
Character mistake: President Marsdin says that Camp David was named by President Eisenhower in honor of his son and grandson. It was actually named for his father and his grandson; his sons were named John and Doud.
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.
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