While Tim Barnett is right in labelling Brash's call for more referenda "desperate", his general objection to referenda is a little over the top:
He said Dr Brash was floating a "very different kind of democracy" where decisions could end up being made by a version of "mob rule".
That very much depends on what sorts of safeguards there are and the balance of power between Parliament and popular votes. The chief worry with referenda is that they could erode the rights of unpopular minorities. A secondary concern is that they could result in contradictory entrenched budgetary demands (as has happened in California). A third is that without spending controls they could simply become a tool for monied interests able to afford expensive publicity campaigns. But on the other hand the Swiss have managed to do them properly with no significant problems for over a hundred years.
I think there's definitely a role for citizen's initiated referenda, either as a direct legislative mechanism or as a "people's veto" on unpopular legislation. The question is how we implement it, not whether we should do it - and it's in that complete and utter lack of detail that Brash's "proposal" really falls down.