When Cara & Clark are talking in the street, Clark's bag changes shoulders with each reverse camera angle.
When Superman flies up to Supergirl while they're saving the Venture, their capes are flying out behind them. However, since Supergirl was actually flying backwards while trying to slow down the falling plane, her cape should be flying the other way, as should Superman's while he's keeping pace with her.
The Venture Spacecraft has large air intake ducts which implies it has jet engines. Jet engines don't work well beyond 100.000 feet above sea level, so it wouldn't be logical to have jets on a spacecraft intended to operate in space more than a million feet above earth.
When she sees the new DEO headquarters, Kara complains about having been bitten by a bat in the previous location. Assuming there was no kryptonite carelessly lying around, her skin is impenetrable; there would be no pain from the bat's fangs for her to feel, and thus no reason to complain.