Genre Turning Point: Part of the reason that this comic was so important was that, for better or for worse, writers realized that they could kill off a major character and just bring them back later. Starting with this, Death Is Cheap has become so prevalent in comics that it's almost impossible to take any death seriously.
At the end of the Justice League America tie-in to "Funeral for a Friend," Booster Gold sits by the comatose Blue Beetle's hospital bed and prays for his recovery after seeing the other heroes all paying tribute to Superman, hoping he won't have to go through another hero's death immediately after, especially if it's his best friend. 13 years later Booster really would end up mourning Blue Beetle after Max Lord put a bullet through Beetle's skull in Countdown to Infinite Crisis.
The Toyman's appearance during "Funeral for a Friend" where he's shown to be mourning Superman's death by noting how he always looked out for kids, in light of his next appearance shortly after the whole "Death of Superman" saga ended which controversially re-imagined him into an Ax-Crazy child murderer.
During "Reign of the Superman" a fan commented in his letter that "It's amazing how far comics have come in twenty years. Then Doomsday would have been some monster thrown from Krypton or something". When Doomsday's origin was eventually revealed, it turned out comics actually hadn't changed that much.
During his fight with Doomsday, Superman muses that he would suspect Luthor was responsible for creating Doomsday if he were still alive. Sure enough, Luthor ended up being the one who created Doomsday in Batman v Superman: Dawn of Justice.
During Adventures of Superman #502 Luthor comments on how he and Superboy are more alike than he thinks. Guess who Superboy later turns out to have part of his DNA cloned from in addition to Superman?
Idiot Ball: Doomsday may be really tough, but he also presented absolutely no threat if he couldn't get within arm's reach of anything. Despite the Justice League having multiple telekinetics at the time, nobody thought of simply picking him up. Granted it probably wouldn't have worked since Doomsday was made unstoppable but point for trying.
As Max Landis "educational parody film" The Death and Return of Superman explains, this wasn't really the attitude of comic book readers at the time. At the time, death wasn't something focused on in comic books, especially the main characters dying. As such, when The Cape himself died, it was a big thing for both readers and people who didn't even bother reading comics. What caused this trope, then? After it happened to Superman, every comic book with a dead character decided that it would be equally cool to return.
The Woobie: Lois Lane. Watching the man she loves fighting and dying while still determined to recording the fight is hard enough, but what made her cross into this territory is that, unlike the other heroes and civilains, she is both completely powerless to do anything and, at this storyline, knows both Superman and Clark Kent. While the story's focus is on actions, poor Lois's grief and pain is detailed very clearly, especially with the four new Superman who crop up later in the story.
Lana Lang and the Kents were also this, as they had to keep secret Superman's real identity after he died. Superman was known to be dead, but Clark wasn't.