Metrics to Study the Bitcoin Economy
Though it might not help much with economics, if you run a node then you can also gather information on orphaned blocks, IP addresses, and unconfirmed transactions (some of which may never confirm, if insufficient transaction fee is paid or the transaction size is too big).

Gathering statistics on Bitcoin is tough, as little can be collected reliably about Bitcoin users. Other questions have looked at that issue here and here.

It's generally impossible to even prove that particular bitcoins have not been destroyed (eg the exchange that apparently lost its wallet when Amazon EC2 crashed), though in some cases proof can be given they were destroyed (where bitcoins are sent to a particular address that nobody can realistically have the private key for). I suppose in that regard it's no different to cash.

You might also be able to get some idea of publicity and levels of user interest from activity levels on bitcointalk.org, reddit.com/r/bitcoin and Google search statistics