There's been a good deal of chatter about this Grant Morrison interview, in which he addresses the inconsistencies between FC, COUNTDOWN and THE DEATH OF THE NEW GODS. (Worth reading: the Funnybook Babylon commentary, here, and its antecedent, here.) As Morrison tells it, the first issue of FC was written before the other two series were conceived of; the idea was that the New Gods would be off-panel and unlike hepatitis B for a few years (aside from the avatars that popped up in the SEVEN SOLDIERS project), so it'd be a shock to see Orion turn up dead in a dumpster at the beginning of FC #1. TRINITY, as I understand, was initially going to be the weekly series that followed 52; then it was bumped for a year by COUNTDOWN, which was intended to get certain ducks in a row for FC and provide a dramatic build-up to it.
Which ducks? That's not clear, but the non-Fourth World threads we've seen from COUNTDOWN so far are basically just the Monitors in general, Nix Uotan and Solomon in particular, the destruction of Earth-51, and the new background for Kamandi. Evidently, somebody in a position of authority radically misunderstood the premises of the project the whole line has been building up to since at least SEVEN SOLDIERS and 52 (I have a feeling that Montoya finding the Kirbytech gun in 52 #4 was one of the first major tremors of FC), and commissioned a 51-issue series and an 8-issue series to "set it up" in ways that directly contradict both FC and each other. The ducks are not just not in a row, they're randomly scattered across the multiverse. If DC is going to sell a complicated, serialized narrative on a week-to-week basis, it's entirely reasonable for readers to demand that it make sense on a week-to-week basis; it's a bad sign that the people reading the work have a clearer sense of how it's supposed to fit together than some of the people making the work.
Yes, the contradictions can be explained away with some difficulty, in a sort of No-Prize way, or simply ignored, as Morrison suggests. And it's worth remembering that the edges of Kirby's Fourth World canon were frayed from the start, and that by the time he wrote and drew the NEW GODS "conclusion" and The Hunger Dogs, there had already been a couple of other Fourth World series--not bad ones, either. There was a 1977 revival of MISTER MIRACLE, initially by Steve Englehart and Marshall Rogers, later by Steve Gerber and Michael Golden. The New Gods first reappeared in 1976 in the last issue of 1ST ISSUE SPECIAL--don't ask--and then in a not-bad series by Gerry Conway and the late, great Don Newton that lasted eight issues before ducking into ADVENTURE COMICS for a couple of issues' worth of "the last battle" and "the end of the war of the New Gods". (It's always the end with this crew.) For that matter, one bit of Fourth World mythology that generally gets taken for granted--the Source Wall, seen throughout DOTNG--wasn't even Kirby's: it was introduced in the distinctly out-of-continuity X-MEN/TEEN TITANS one-shot.
(FC and its associated titles, in fact, are something like the third full-scale post-Kirby Fourth World revival. In 1988, there was Jim Starlin and Mike Mignola's COSMIC ODYSSEY miniseries [and the Forever People's six-issue miniseries by J.M. DeMatteis and Paris Cullins], followed by NEW GODS and MISTER MIRACLE series; both NEW GODS and MISTER MIRACLE reappeared in the mid-'90s, then effectively merged into JACK KIRBY'S FOURTH WORLD.)
Perhaps a less frustrating way to deal with the contradictions is not to try to explain them but to accept them as a pesky but integral part of the story, a sort of continuity koan. Continuity is at least sort of mutable--rarely more explicitly so than in Morrison's superhero comics. The prolegomenon to FINAL CRISIS is SEVEN SOLDIERS: MISTER MIRACLE, in which Shilo Norman's many alternate lives both do and don't happen. "Hypertime" is one way of putting it; another is to say that all stories are more or less true, but better stories, more satisfying stories, are more true in the long term.
Update on that contest: I've recently come into possession of a few boxes of good comics from the '80s, many of which duplicate stuff I already owned. The winners of each of the three parts of the contest will get to pick a batch for themselves. Again, the deadline to enter is June 25, and the three questions you're trying to answer most accurately are:
1) How many issues of additional FINAL CRISIS tie-ins will be announced after April 30 but before the end of the series? (Three have been added so far--although neither FC: SUBMIT nor FC: SUPERMAN BEYOND #2 appear on the September solicitations. "Aftermath" titles don't count.)
2) Which will be the first issue of FINAL CRISIS or its associated titles to be released later than its scheduled ship week?
3) When will the final issue of FINAL CRISIS be released? [This contest is now closed.]