Update (June 1, 2017): there is a Visual Studio 2015 version available here.
If you are using Visual Studio 2017 (along with TypeScript) for all your Web development, you have certainty discovered that it is lacking in (for me) one important aspect: linting your TypeScript with tslint.
I looked at several solutions and after not being completely satisfied with any of them, I decided do develop my own. Now, I haven’t programmed in C# for a long time and never implemented Visual Studio extension before, but after a few days of learning and coding I believe the extension is at a point of starting to be really useful. Extension is automated and tries to do as much things in asynchronous way as possible.
You can download the extension on the marketplace.
You can look at the source code, submit issues and feature requests on GitHub.