Starring: Calista Flockhart, Melissa Benoist, Mehcad Brooks, David Harewood
Visible crew/equipment: When Winn is putting on his shirt after being caught, you can see his mic wire through the hole where Kara says he forgot to button his shirt. (00:03:15)
Continuity mistake: When Cat is on the talk show, the microphone on her collar keeps disappearing and reappearing between shots.
The Adventures of Supergirl - S2-E1
Trivia: When Cat Grant walks to her office door, she screams out, "Miss Teschmacher!" In Superman and Superman 2, Miss Teschmacher was Lex Luthor's assistant and him screaming her name was his way of getting her to run to him.
Question: Why did they change her costume and hair style?
Answer: I can't say for certain, so I'm surmising that the change was to "catch up" with the other Arrowverse shows, particularly Arrow and The Flash, whose lead characters have undergone various upgrades and redesigns of their superhero suits over the years; after four seasons, Kara's probably just felt a little stale. And I believe the change in hairstyle was Melissa Benoist's personal decision and had nothing to do with the character.
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.