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

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.

Cataclysm is more prone to these issues because (a) the quest structure across each zone is very linear and each successive quest depends on those that come before, and (b) it is easy to see how many quests are expected to be completed in each zone. However I don't believe it is a bug, but more likely you missing a particular quest stage that results in others not being available.

For Deepholm, one known cause of problems is that one quest needed for continuation of a quest change is a drop - http://www.wowhead.com/item=60816. If you didn't loot this or it didn't drop for you at the appropriate time you can end up stuck. I would suggest attempting to gather this item and see if it opens up more quests if you have not already.

There are a number of similar situations in Uldum (http://www.wowhead.com/zone=5034#starts-quest) lists the items that can start quests there. Another issue that I've noticed is that some people enter directly into Uldum, without using Blizzard's "entrance" quest where you guard a caravan on its trip into Uldum from Tanaris. If you did not complete this, some quests will be unavailable.

I hope this helps with your issues. It is fair more likely to be something similar to those than a bug, and there are definitely no maximum level limitations.