The main costs in onshore wind are the grid connection and the cost of steel & fabrication of the tower sections. Between them, over 50% of the cost of the resulting energy. There is progress being made still in lighter, more flexible towers, but I'm not sure how much further there is to go; these days a 1% gain is a big win, while ten years ago a 10% gain was perfectly feasible (eg individual pitch control reduced tower loads by ~ 10-15%). The cost of the grid connection is largely out of the control of the project developer and no-one who is able to reduce it has any incentive to reduce it, so don't look for big savings there. Sure, there's another 40% or so of the costs that can be optimised, but that's spread over lots of small things, so eg halving the O&M costs will not make a big difference to the overall cost of energy. It's hard to see steel getting a lot cheaper than it is, so it seems likely that onshore wind is approaching its long-term cost.
Offshore is another matter. An offshore turbine is just an onshore turbine that's bolted to a support structure that's in the water (more or less) so the costs of the turbine itself are pretty similar to onshore. The main thing holding up the cost of offshore wind is being able to hire a suitable construction ship on a day when the whether is suitable. So yes, development of specialised construction ships that can operate in worse weather, and expansion of the fleet of such ships, is the big factor in bringing that cost down - though it's unlikely to ever match onshore wind. Floating turbines are also a concept that cuts these costs significantly - no need to drive piles into the ocean bed to anchor the support structure - though you do still need some seabed structure for the grid connection etc. I don't think anyone's quite ready to start building large fleets of these (though there are plenty of prototypes around).
Grid connection is a bugger, whether it's for a grid-scale wind farm or a residential solar panel. Way too much of the cost of these systems is just getting the thing connected to the grid. Feed-in-tariffs don't help here, as they make the metering more complicated (you have to measure imported and exported power separately, instead of just measuring net power imports). Someone ought to do something about that. Cheaper inverters and simpler meters FTW.