Factual error: The Marine Colonel in Supergirl played by Eddie McClintock spends all of his time wearing Marine Officer's Dress Blue Bravos. Marine Dress Blues are ceremonial uniforms. On rare occasions, the Charlies or Deltas (no coat) may be worn as a work uniforms (the primary exception to this rareness being recruiters). The full uniform is certainly not worn for day to day work in the field.
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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.
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Other mistake: During an argument, Maggie's father mentions the border wall being built to keep Mexicans out of the country. This is obviously a reference to the real-life presidency of Donald Trump, but within the show's continuity, his comment doesn't make sense: in "Resist", the penultimate episode of season two, it's revealed that President Olivia Marsdin is literally an alien from outer space, and earlier in the season in "Welcome to Earth", she signed an executive order offering aliens such as herself full citizenship if they so desired it. If she's that tolerant of extraterrestrials, it seems unlikely that she'd be so intolerant of foreign immigrants as to resort to such an extreme action in foreign policy like building a wall on the border.
Continuity mistake: Mike and Kara are in the alien bar in the both talking about Mike not controlling his powers. When Mike breaks the glass there is no other glass on the table. In the next shot a glass appears at the edge of the table, in the next shot the glass is gone again.
Continuity mistake: When J'onn J'onzz is fighting Miss Martian in the ring, she punches him into a wall, leaving a massive dent. She missed the next punch, and the plaster on the right hand side of the dent falls out, but the plaster on the left is fine. Miss Martian then throws J'onn across the room, and in the background, the dent is visible, but it is now the left hand side of the dent where the plastering is missing and the plastering on the right is now mostly in place.
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