For the Girl Who Has Everything - S1-E13
Other mistake: In Kara's hallucinations of Krypton, the planet is shown with a yellow sun. Rao, the supergiant around which Krypton orbited, was red.
Continuity mistake: As Kenny is about to sit down opposite to Kara, the juice on his tray is lying down on it. Next shot it is standing up.
Homecoming - S2-E14
Continuity mistake: In the scene at the end where Mon-El goes to Kara's to try and console her, right after he sits down and she shifts to lean on him the blanket falls off her shoulder, but in the next shot it's covering her once again. (00:40:35)
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.
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.
Other mistake: During the boardroom meeting with Lena, James, and Morgan Edge, Katie McGrath's natural Irish accent briefly, but noticeably, slips out.
Plot hole: After Kara and Alex are run off the road, Kara is convinced by "Noel Neill", revealed later to be J'onn, to stop using her powers. From context, J'onn had to have been summoned by Eliza, but in 2007, she would still think he's just Hank Henshaw; she doesn't learn he's not, or even that he's a shapeshifter, until 2016, as seen in season 1's "Myriad", well after Kara and Alex have grown up.
Answer: Yes, s02e22. As Kara leaves her office, she said "go get them, Supergirl" to herself. After season 1, the show switched from a CBS production to a CW production and filming moved from L.A. to Vancouver. Flockhart isn't really a fan of traveling to shoot, and didn't want to be away from her family for so long.
Bishop73