Supergirl/Fridge

Fridge Brilliance

 * Silver Age Superman is often mocked or bashed by sending his fifteen-year-old orphan cousin to an orphanage. However, Superman volume 1 #149: The Death of Superman! shows that Superman's fears weren't unfounded. In that Alternate Universe tale, Lex Luthor manages to murder Superman, but he doesn't get away with his crime because Supergirl -whose existence he was unaware of- captures him.
 * During the Silver Age Supergirl grew up and become an adult woman. However Superman hardly changed. Posterior canon has established that Kryptonians age more slowly under a yellow sun after reaching adulthood, so it makes sense she got older although her cousin did not.
 * In Many Happy Returns, Linda Danvers tries to take Earth-1 Kara Zor-El's place and fight the Anti-Monitor but her plan fails. If you think about it, she was doomed to failure: Kara could fight the Anti-Monitor because she was a virtual Physical Goddess. Linda is a powerful human. She had no one prayer.
 * In Supergirl volume 5 #0, Post-Crisis Supergirl spots Lex Luthor's spy satellite, but Lex refuses to believe this. It makes perfect sense: Lex is supremely arrogant and he'd never believe an alien can beat his technology.
 * Post-Flashpoint Supergirl didn't trusting Superman at the beginning becomes understandable given the craziness of his claims, and his Kryptonian accent is terrible. Also, he could be a clone or genetically engineered figure. And this is exactly what H'El turns out to be.

Fridge Horror

 * Several Post-Crisis stories imply that Kara's ghost keeps wandering over New-Earth. What if she saw everything what happened between Linda and her younger self in Many Happy Returns?
 * Infinite Crisis came out less than two years after the end of Many Happy Returns. The four survivors of The Multiverse saw that story's events playing out. Earth-Two Superman watched how his Earth-One cousin -whom he owed his life- was ignored by Post-Crisis Superman and hurt and mistreated by other people -who were alive thanks to her- and the human girl who took up the Supergirl's mantle got screwed-up. Undoubtedly it convinced him that Earth could not be saved.