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.
Plot hole: After Barry and Kara slow time everyone is slow, even Superman, but Oliver could move fast enough to shoot an arrow.
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.
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