One of NoSQL's goals: handle previously-unthinkable amounts of data.
One of unthinkable-amounts-of-data's problems: previously-improbable events become extremely probable, precisely because the set of interactions is so large. Flip a coin a hundred times, and you're not likely to get 50 heads in a row. But flip it a few trillion times, and you probably will find some 50-heads streaks.
So NoSQL's performance strength is also its mathematical weakness.
This order of scale can result in lots of problems, but one of the most common is consistency -- the C in ACID -- clearly a fundamental desideratum for any database system, but in principle much harder to acheive for NoSQL databases than for others.
Emerging database technologies have forced developers and computer scientists to define more exactly what kind of consistency is really needed, for any given application. Two years ago, ACM (the Association for Computing Machinery) published an extremely helpful examination of the attenuated notion of consistency called 'eventual consistency'. Their summary:
Data inconsistency in large-scale reliable distributed systems must be tolerated for two reasons: improving read and write performance under highly concurrent conditions; and handling partition cases where a majority model would render part of the system unavailable even though the nodes are up and running.
The article surveys technical solutions as well as user considerations that might soften the undesirability of anything less than perfect, instantaneous consistency. It's not long (4 pages plus pictures), and explains some deep database issues quite clearly.
On the more practical side of the problem: Russell Brown recently gave a talk at the NoSQL Exchange 2011 on exactly this topic. More specifically, he showed how some distributed systems (Riak in particular) try to minimize conflicts, and suggested some ways to reconcile conflicts automatically using smart semantic techniques.
Check out the NoSQL Exchange page for Russell's talk here, which includes an embedded video. But read the ACM article first for a broader overview, since Russell launches into technical details pretty quickly.