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.
Continuity mistake: During the fight between Supergirl and her clone, the clone blasts Supergirl with her purple lightning power, which causes a small explosion and also somehow turns the sky from bright dusk to nighttime.
O Brother, Where Art Thou? - S4-E15
Factual error: While the location of National City is never revealed, it is generally accepted that it is located in the US. But all the helicopters used to fly Lex around are Canadian.
Other mistake: J'onn J'onzz starts a private Investigation company. He is shown looking at the new PI license he just placed on the wall. But the certificate says it is a renewal. (00:05:30)
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.
Answer: Another part of why the change was that it's cold in Canada in the winter and the old costume didn't protect her from it, whereas the new one is nice and warm.