This requires delicate handling of type definitions which collide, because
we use TypeScript-provided lib.d.ts for --target=es5 and lib.es6.d.ts for
--target=es6.
We need to include our polyfill typings only in the --target=es5 case,
and the usages have to be consistent with lib.es6.d.ts.
Also starting with this change we now typecheck additional modules,
so this fixes a bunch of wrong typings which were never checked before.
Fixes#3178
This uses tsd to fetch the typings from another git repo. I've forked the DefinitelyTyped repo because some typings we use are not available upstream.
We should probably fork it in the Angular org, so everyone on the team has commit access to our DefinitelyTyped fork.