World-of-warcraft – Cannot play random Cataclysm dungeon

I'd suggest not being grouped. Then have the lower level player 'tag' the mob e.g. by putting an instant cast on them or a DOT. Once that starts doing damage, the nameplate of the mob will turn grey for the higher level player. At this point the lower level will be the one who'll be credited with the XP for the kill, Now have the higher level AoE them down. That way there should be no XP penalty and fast kills.

I'm sure I remember people using this approach to get the fastest time to the level cap, by tagging things and having an army of friends / guild members burning them down. Link to a discussion of this: http://dwarfpriest.com/2008/04/30/mythbusting-1-70-in-a-day/

On March 19th, the German player Tosog broke all of Athene’s supposed records. He reached 70 in 1 day 4 hours and 20 minutes (video here of him hitting 70).

He admitted to being boosted by other players to reach 70 so quickly (he had higher level players (not grouped with him) kill off mobs he tagged). This was a respectable coordinated effort between multiple players.

It was considered a borderline exploit in the 'fastest to the cap' race I think.

I'll address each of your questions one-by-one, as there seems to be some confusion:

What is preventing players from receiving new quests in the new 80-85 Cataclysm zones?

There are several reasons why you may not find any quests in a zone where you know you should have quests:

• Quest-givers that have quests that significantly below your current level will no longer show up on the minimap and will not have exclamation marks above their heads unless you check low-level quests in the minimap tracker.
• Certain quest hubs will only unlock when you complete a so-called breadcrumb quest: this is especially true in Cataclysm. You might be overlooking one quest somewhere relatively off-the-beaten path that's preventing a whole slew of quests from opening up.
• You're in the middle of a phased quest chain. See what happens if you complete the quests you already have, or abandon quests.

Is it a bug that has not been smashed or confirmed by Blizzard yet?

There is no bug confirmed by Blizzard about not receiving quests. The fact that thousands of people have been able to quest without issue is a good sign it's something you're missing with your specific situation, like the scenarios outlined above.

Are there level caps for each of the new zones released with Cataclysm?

There isn't a level cap that prevents you from picking up quests: you can pick up level 1 quests even at level 85.

Will I be able to come back though and pick of these missing quest for each zone after hitting level 85?

Yes. In fact, I just did that with two of my characters.

Are there others who had similar issue but it was resolve after hitting 85?

In the comments on this answer, you mentioned that you have found others with the same problem as yours, so presumably that's the answer. As mentioned above, it's not particularly widespread and there may be something you and others in the same boat have overlooked (it happens to the best of us).

Is it [the Warchief's] fault?

Probably not.