I'd say that if you are working with diverse documents with a few or no relationships, a document oriented database is necessarily a better fit to the task at hand than a relational one. It's a tautology.
If you are needing many JOINS and your data is homogeneous, there's a mismatch. You probably should have chosen a relational database in the first place, as it better fits that model.
Durable ? NO. It is trivial to distribute data between multiple nodes using MongoDB and have writes be on some or all of them. I have yet to see a clustering SQL system that makes the process as simple as any NoSQL database.
Fewer application errors ? Well this just makes no sense. Why would a database be causing application errors ? Either the fetch/store request fails or it doesn't.
Lower TCO ? NO. MongoDB has an order of magnitude less TCO than any database I've used. Period. It is trivial to cluster, shard, deploy, manage and being schema-less there are no migrations to worry about. Ease of use is one of the big reasons why MongoDB is popular right now.
And PostgreSQL HSTORE seems like a bit of a hack to me. It has a ridiculously complex syntax and still not sure how it handles querying other data types e.g. dates.
The thing is, an RDBMS really is a superset of most of the other data models floating out there.. Entity-attribute-value, Document, plain key-value, whatever. Your every day ordinary RDBMS can do it, with transactions, durability, ease of administration, whatever. When you use a NoSQL data storage system you're explicitly trading off one or more of the capabilities of an RDBMS to get some other benefit. The one thing that Postgres isn't good at, as far as I know, is a graph-like data structure.