Looking for an answer to this question since I heard of .NET 4.5.1, I've nearly given up the hope. Looks like no one has written anything about this anywhere. So now that 4.5.1 and VS2013 were released... Is it possible to switch SP to the new .NET Framework and use this long awaited feature, Edit & Continue, in SharePoint? It works in ASP.NET too.
Update: Just installing VS2013 and testing a previous solution did not work. Obviously you have to change SP to somehow use 4.5.1.
Creating a new SP Project targetting 4.5.1 does not work.