It looks like their demise was due to fraud/embezzlement. Not sure how bitcoin would help here.
Also, users of such an exchange would be heavily exposed to the volatility of BTC/$major_currency when making long-term bets. Unless one doesn't care about currency risk, but it's not easy to ignore it unless as long as one's future expenses are still pegged to $major_currency.
The Bitcoin protocol has built into it a sophisticated scripting component which would make it possible to make multiparty contracts (like those on a predictions market) that could not be broken by any means, other than an attack on the underlying Bitcoin protocol. It hasn't yet been fully implemented in any client, but it's there to be used whenever the devs feel comfortable putting it in. This feature has the potential to make Bitcoin fraud/embezzlement much more difficult than it is now.
Also, users of such an exchange would be heavily exposed to the volatility of BTC/$major_currency when making long-term bets. Unless one doesn't care about currency risk, but it's not easy to ignore it unless as long as one's future expenses are still pegged to $major_currency.