The resulting hash of a multihash function (including multiple iterations) has the same collision resistance as the collision resistance of the weakest hash.
This is not exactly true, the collision resistance is weaker than the weakest.
Just to be clear, for practical purposes what knightdk says is true. But from a cryptoanalysis point of view, it's slightly more likely to have a collision.
Another idea: if the NSA has a backdoor for sha256, then it is possible that backdoor doesn't work for double sha256.