So right off the bat, you've lost the querying power that SQL offers. When dealing with data that's intended to be analyzed, that sounds like a pretty big loss.
Clearly its built-in sharding support, which is often touted as one of its biggest benefits, wasn't suitable for you. So you had to invest some time and effort coming up with an alternate system. That sounds like a loss to me.
When it comes to the schema issue, it sounds like you haven't actually reduced the effort or work in any way, but merely pushed it somewhere else. Like you admit, you still do have to deal with the schema, it's just handled within the application logic, rather than the database. That sounds worse to me, especially if there is more than one application using the database.
right off the bat, you've lost the querying power that SQL offers.
Can you point me to any reasonably-priced database systems that allow me to execute SQL queries against a cluster of shared-nothing machines running commodity hardware? I'm not interested in paying $20-100K/TB/year for Vertica and friends.
SQL can be great if you have vast amounts of money or if your data can fit onto a single machine. When neither of those things are true though, nosql DBs become important.
Well are we talking with shard capabilities built-in, or having to roll your own? If you can roll your own then I suggest looking at Galera (we use this for our production MySQL stuff) http://www.codership.com
If it has to have built-in sharding then I can't think of anything off-hand.
MySQL cluster is another option beyond MySQL Galera (and Cluster actually has a NoSQL layer on top of it.. FYI)... but I have to say if we want to talk about scaling issues for MongoDB, you might not be happy with some of the limitations of NDB.