The main argument against, as I see it, is the lack of accountability, the prime example being California demanding more spending and lower taxes at the same time. Of course, indirect democracy has done very little to prevent that either.
When Switzerland doesn't pass laws similar to California's, I think it's because they have a much more homogenous society where there is simply a large degree of agreement on how things should be done - and so, the remaining bits lend themselves well to be decided by direct democracy.
That's also my response to the GP: no, no amount of interwebs and technology can turn a large and diverse population that disagrees fundamentally on many important issues into a small and homogenous one that agrees on most things.