The main issue is going to be, that when decisions are made based on popularity and only those the most engaged are participating, the decision is going to be decided by extremists. This somewhat sabotages democracy, as the representative democracy counterbalances those on the fringes with the lethargic majority.
Issue based politics is leading to a lot of problems, i.e. if you would put it to a popular vote, I am quite confident that the death penalty would be back at least in some European countries for child molesters, etc. Popular opinion seems very volatile and if you are able to time your issue driven vote with some incidents of public outrage, you can pretty much able to pass highly questionable ideas. Of cause there is the hope that bad decisions will "teach" voters to do better next time, but (at least in my opinion) there are not many signs that this learning effect takes place with the current party/election system.