Is there a place or tool to monitor all addresses for unmoved coins?
In aggregate, this is shown in BitcoinDays Destroyed (e.g., unspent for one year or more).

This can be done with some degree of effort using the Bitcoin API.

v0.7 getrawtransaction gives you access to transactions even those not in your wallet.


http://en.bitcoin.it/wiki/Raw_Transactions


There are other tools that you can use to build this capability as well.


libBitcoin
Armory (see Extras)
Bitcoin ABE