Yes, I can't come up with original content on my own, so I'm stealing something I read on another, smarter blog! That's just what I do!
As it is, the best I can do is suggest that the somewhat contradictory depictions of Orion and Darkseid's last-last-last battle that we witnessed in Countdown and DOTNG recently were apocryphal attempts to describe an indescribable cosmic event.
What keen eyes that crazy Mr. Callahan has! "Apocryphal continuity" is a nifty idea, because it allows us to explain away stupid stories. He asks, and so will I, what you think are good ideas of "apocryphal continuity."
I'm going to lay one ground rule: This does NOT mean any story you happen to dislike. This means, to me, any story where the explanation is so idiotic it must be because the writer was trying to describe an event for which he had no words. We should treat the event as something that actually happened, but the writer couldn't explain it. Like ancient writers trying to figure out where lightning comes from, for instance. So the story could even be something you like, but the explanation has to be absolutely mind-bogglingly stupid. Off the top of my head, I would suggest Superman changing reality by punching it to be an event that the writer just didn't understand, so he "made up" the story about an inordinately strong man punching the walls of reality.
You might not like the God of All Comics, but you have to love the way he explains why things don't jive with his version of things! So what are your examples of "apocryphal continuity"?