This metric may deal with one issue, but it is still totally useless as an objective metric of 'the bitcoin economy'. A much more reality-based metric would be the number of retailers (etc) accepting payments in BTC (and their volumes if they were available). But this would be a much more sobering picture.
I agree its still a flawed metric. Your example of the same bitcoins being used in multiple transfers, in the one day, seems completely valid to me.
But I don't think there's a perfect way of measuring the velocity, unless you've a complete map of addresses-to-identities, which isn't available (and even that is neglecting transactions done within exchanges, that aren't backended onto the bitcoin system - which is probably a fair enough limitation.)
The same is true, if you are trying to calcuate velocity of money in any traditional economy, where cash transactions are permitted. The cash could be used in several transactions between observations - theres no way of telling - and theres nothing that can be done to solve that. So, such measures are always going to be approximate.
On this topic, something that surprised me recently, was the assertion in Paul Krugmans blog http://krugman.blogs.nytimes.com/2011/09/07/golden-cyberfett... "The actual value of transactions in Bitcoins has fallen rather than rising. In effect, real gross Bitcoin product has fallen sharply. "
I'd love to know how he came to that conclusion, or what sort of data he used, and whether its accurate.
Fair enough, but its a measure vulnerable to the problem that days-destroyed is trying to solve - it'd be easy for people currently sitting on large volumes of Bitcoin to 'solve the problem' that is highlighted by Krugman, by just shuffling their coins around.
I'm not sure if this metric is useful, but it is interesting to see if the early users start to 'cash out'.