I still don't see where could be the problem)
Everything is similar to the current implementation of btc. Each block contain hash of previous and hash of concatenation of the all balances and proof of work of this block.
So block 123,456 shows I (or more correctly an address I have) have a balance of 100 BTC. How do you verify it? If all you have is the balance how do you know it is correct?
I can be sure that longest blockchain without its last 256 blocks is correct with prob > 1-2^(-256) (so it is easier to break some sha-256 from the network). When I get longest blockchain and transactions during last 256 blocks I can easily check if the transactions are correct and then check if the last 256 blocks are correct (that they are calculated from correct balances and check proof of work).
The problem that I see is that each adress actually still need to remember last balance before last 256 blocks of each address (remember only self balances and hashes of concat. balances of each block is not sufficient). But nevertheless it still seems to be much less to store then each transaction.