Armed robbers aimed their shots at Kara's chest; only her cape got bullet holes.
Kara sometimes grunts when struck while fighting. But not when she's run into by large trucks.
A 4 engine passenger jet can lose one, even two engines and make a controlled landing.
Kara states that the stylized S on her outfit is the family symbol for the House of El. The stylized S was created by Martha Kent, the adoptive mother of Kal-El (Superman/Clark Kent) in the Silver Age comic books, but the pilot draws on later interpretations of the symbol that appear in both the comics and other media. As shown in previous films and in the current comic story lines, the symbol is known as a coat of arms for the House of El as well as a symbol of hope.
Kara is bulletproof as shown during scene at bank robbery, yet the DEO captures her by piercing her with syringes. The syringes are filled with kryptonite, which weakens her powers, thus allowing the syringe to penetrate her skin. This trick has been used against Superman in multiple adaptations.
Kara wears glasses while working at Catco however she doesn't decide to become a hero until after she saves her sister's plane from crashing so there would have been no need for her to wear glasses for a disguise (like Clark Kent does). The origin and purpose for the glasses is explained later in the series.
In the Silver Age comics, Kara's Earth name is Linda Lee Danvers, not Kara Danvers, and she grew up in an orphanage. However in the contemporary stories, she went for a long time without a secret identity before adopting the alias Linda Lang. The pilot chooses to dub her Kara Danvers, combining her Kryptonian and adoptive names, likely in order to simplify the situation for the audience.
Supergirl's origin story has been revised several times since the character was created. In the original story her family was saved when their city, Argo, was blown away from Krypton intact during its destruction, and she was sent to Earth several years later when kryptonite radiation threatened the city's inhabitants. The pilot episode draws on the current origin story, which is essentially identical to Kara's narrative.
A character crashes through a cinder block wall that wobbles and flexes on impact.
In the opening monologue of the series, Kara Zor-El states that Krypton was destroyed 24 years ago as she was leaving the planet and getting trapped in the Phantom Zone as a 13 year old girl. She them mentions in the same monologue that she arrived on Earth "2 Dozen" years after her cousin, while still a 13 year old girl, and this series appears to take place at least 10 years after she arrived on Earth.
Kara's ears are pierced, which would be extremely difficult to do given her invulnerability. It's implied that she has had little contact with her cousin, nor access to the Kryptonian materials in her ship, either of which would be necessary in order to pierce her ears. She also states that she hasn't felt pain before, implying that nothing has ever pierced her skin. When she is shown on Krypton, her ears are not pierced, so it could not have been done before she gained her powers.
Kara states that she has never felt pain before, but she would have had at least some experience with it before coming to Earth and gaining her powers. Kryptonians are not naturally invulnerable to pain, and Kara lived for 13 years as a "normal" child on Krypton.
If the distance between Krypton and Earth is 2,000 light-years then neither of the "supers" should have arrived on Earth for at least 2,000 years and, most certainly, many, many times longer
than that.
Kara hugs her sister so hard that bones can be heard breaking but her sister just shrugs
it off.
In the opening scene, Kara says that it was 24 years since Krypton was destroyed. If Krypton was destroyed 24 years ago and Clark had already become Superman, then she can't also be 24. She was trapped in the phantom zone, NOT aging, for 24 years, so she would have still been 13 when the show starts. Also, in the season with Reign when they show the years since Krypton was destroyed, it CLEARLY says 35 years which means Kara SHOULD have said 34 years ago, which actually lines up the timeline.