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Google Analytics counts all hits, not just the ones generated by google serps.
In 50 days 680 visitors sent by search engines is quite allright - but where does the rest come from? Are you sure you're not counting robots as visitors? Google, yahoo and msn might hit your site pretty hard and if you don't filter them, you'll have much higher visitor numbers than you actually do. Might be worth a check, though the outcome might be depressing ;)
As far as your low percentage of inbound traffic from SEs, this is pretty normal as you begin to be able to get ranked, in my opinion. Are you only ranking/getting traffic for brand terms right now?
I am getting traffic based on current news & event keywords like for instance Apple has recently announced iPhone 3G so I get traffic on this keyword.