In the common route, you have to make the correct choice in order to unlock a character's route. This choice actually foreshadows the remainder of the route. Big spoilers ahead if you have not played the route.
"I want to trust you." to Mineo Enomoto. This choice is crucial because Ichika decides to trust him, somehow able to see past his uselessness. His route focuses on coming to trust you as his partner. Her faith that he is more capable than he lets on helps him can climb out of the pit of inaction he put himself in.
"Do you suspect me?" to Takeru Sasazuka. This choice shows that Ichika is intelligent enough to see the reason behind Sasazuka's actions. He agrees that he suspects her, but also expresses that Ichika is naive and not cautious enough. His route then focuses on his true motivations behind investigating the X-Day incidents and whether or not you suspect him of becoming a true sympathizer of Adonis instead. In the rest of the route, he also learns to respect your intelligence, judgment, and capabilities, which he doubted when he suspected you.
"What are you trying to protect?" to Kei Okazaki. His route focuses on him looking for something so worthy of being protected that he could give his life up for it. The protagonist becomes this, but then she has to fight his Death Seeker attitude.
"Speak honestly." to Kageyuki Shiraishi. Ichika has to spend the whole route dealing with a Kageyuki who is so brutally honest that he's callous at times. In turn, to earn Shiraishi's trust and thereby good ending, Ichika has to choose to be honest with him, despite his teasing. It eventually turns out that despite how honest he seems at surface level, Shiraishi is incapable of being honest to himself and Ichika has to break the mask he has been maintaining.
Finally, Yanagi's route: To unlock it, you have to finish all four of the other routes. In order to officially enter his route afterwards, you have to answer four back-to-back deduction questions regarding the motivations behind X-Day correctly. This knowledge could only have come from playing the other four routes. Accordingly, Yanagi's route gets to the bottom of the X-Day Incidents and by the end of the route, all of the issues the other characters have been facing have been addressed.
Mineo's route involves Adonis falling apart before the climax of the route for inexplicable reasons. It turns out that this is because Yuzuru, who's revealed to be Zero in Yanagi's route, was shot and ended up in a coma. Without their leader, Adonis couldn't continue his plans.
Cats as an Animal Motif is abound in the game but doesn't make a big impact to the story... unless one counts the SchrodingersCat. Your choices as Ichika will determine to whether you can advance further or be stopped in virtue of choosing choices that led to a bad ending. And should you choose a choice that leads to that bad ending after seeing how the ending goes, the text glows.
Early on in Sasazuka's route, he asks what is Ichika's talent. Choosing "Shooting" will lead to some sort of Bad Ending eventually. Sasazuka Does Not Like Guns due to what happened to his mother and Ichika essentially boosting that using guns is her main strength will not endear her to him.
Think about poor Kazuki and how he must feel in all of the bad ends. Or heck, how about Shiraishi's Good End where Shiraishi keeps his amnesiac sister underground for a year for his own selfish reason of being with her through her recovery. Yanagi and his team even helps Shiraishi in this, but never head down to see her for whatever reason. Kazuki only gets to see her a year after all that!
