After Flashpoint, it was known by several of the heroes that Diggle's daughter Sara was wiped from the timeline and replaced by a son, John Junior. Post-Crisis, both Sara & John Junior exist — of course Oliver would make sure his best friend had both of his children in the new universe.
The fact that nobody but the Paragons and the people whose memories J'onn restores remember the Crisis and the destruction of the Multiverse means that none of the other shows and movies involved in the crossover have any need to acknowledge the events of this crossover, or let them affect their own continuity.
Viewers point out that the chairs for the League's round table resemble gamer chairs. They quite possibly are—several members of Team Flash, including Barry himself and Cisco especially, are canonically otakus and gamers.
Superman Returns was supposed to ignore the events of Superman III and Superman IV: The Quest for Peace, but Routh Superman makes an obvious nod to the third movie. But at the end of Hour Five, it's implied that the gassing of the Daily Planet never happened; so if Earth-96's history has been altered, it stands to reason to assume that the third and fourth movies happened on Pre-Crisis Earth-96, but were erased following the restoration of the multiverse.
Fridge Horror
Alex, Diggle and the other characters who aren't Paragons don't remember the Crisis until J'onn telepathically implants the memories in their head. This means that they've all grown up on Earth-Prime, and are essentially Replacement Goldfish for the characters we've been watching for the past several years, all of whom are now dead. They may well have completely different memories and pasts from the people that Barry, Kara and the others remember.
