The president's "Alien Amnesty Act" is described as an executive order: a change imposed solely by the executive branch of the U.S. government. But the term "act" refers to a law passed by Congress, the legislative branch.
In her speech, the president describes Ellis Island as a place where *thousands* of immigrants came to America. In reality, the number was in the *millions*. In a speech designed to praise immigration, she would almost certainly have used the correct, larger number.
Lena Luther says that plumerias (the flowers on her office desk) are pretty rare. However they can be found in tropical climates such as Hawaii, Mexico, and Central America.
The night sky above the observatory was obviously added in during post production. A nebula, with all its colors, can be seen in the sky. However there are not any nebula close enough to Earth to be seen with the naked eye. And even when viewed through a telescope it wouldn't have the color detail seen, as most of the color wavelengths would get reflected by the atmosphere.
During an attack, DEO Alex Danvers (a regular human without any supernatural powers) is hit face front by what can only be described as a literal "ball of fire" so forceful it hurls her back into the air. And yet she not only gets up straight away like nothing happened, there isn't even a burn mark on her.
Kara is normally above prejudice, but the moment she found out Mon-El was from Daxam, she outright blames him for the attack on the president; no evidence of him making any with attempts or having weapons nor powers related to heat. The only things Mon-El was guilty of was property damage and strong arming an astrologist into broadcasting a distress signal. Kara outright ignores that Mon-El was only lashing out at her at first due to confusion and would understandably keep a low profile to figure out a way OFF the planet.