I'm attempting to get an ASP.NET Core 1 solution to work on both Mac/Windows, but I am having issues with it. I am working with Mac Visual Studio Version Preview 1 (7.0 build 347) and Windows Visual Studio Version 4.6.01586.

You can use Xamarin Studio and Mono to make a winform app for mac, though if you want to to use Visual Studio buy Xamarin business license for VS support or make a XNA or a web app. See my answer here.net core for linux and mac for more info.

Microsoft Visual Studio For Mac

When I attempt to open/compile the ASP.NET Core 1 application from Windows to Mac it tells me to 'Please build the project and retry, or set the OutputPath and AssemblyName properties appropriately to point at the correct location for the target assembly' but when I try to build it doesn't work (it skips).

Vice versa, when I try it from Mac to Windows it doesn't even open and it comes up with the error message 'Error while trying to load the project '.../ASPNETCoreWindows.xproj': Unknown solution item type.

Visual Studio

Visual Studio For Mac Os

Not sure if the different version types plays any role in this, but I also noticed that the Mac version doesn't include a project.json. For reference, I have two blank ASP.NET that can be used for testing:
https://github.com/ChristianRRL/ASPNETCoreWindows/
https://github.com/ChristianRRL/ASPNETCoreMac/