Net neutrality would give regulators significantly more power over how ISPs operate their networks. Due to regulatory capture[0], we can expect those regulators to advance the interests of entrenched players over potential newcomers.
So the biggest costs are probably Bastiat's "unseen" [1] costs. The things that could have been but never will. We may be helping lock in the ISP industry of 2014 as a permanent status quo.
I would argue that net neutrality is a shortsighted compromise. Instead of trying to make the monopolists be slightly less bad, we should be legalizing real competition for them.
For example, if the goal is really to improve service and reduce costs, we should be campaigning to legalize municipal networks at least as hard as people are campaigning for net neutrality. Why is net neutrality getting attention and these other barriers aren't? Because there are big commercial interests who benefit from net neutrality.
[0] https://en.wikipedia.org/wiki/Regulatory_capture
[1] http://bastiat.org/en/twisatwins.html