All parts of the Web Components specification aren't implemented across all of today's browsers, or else aren't enabled by default.

Chrome 36+ is fully capable of using Web Components by default (including Dartium). Firefox requires that you enable it manually. No matter what browser you're using, there's a polyfill that enables Web Components in most browsers (https://github.com/WebComponents/webcomponentsjs).

Dart Pub already contains this JavaScript library along with a small script that is required when using the compiled version from dart2js. Add web_components to your dependencies and include the polyfill JavaScripts in your page:

<script src="packages/web_components/webcomponents.js"></script>
<script src="packages/web_components/dart_support.js"></script>

For an up-to-date status about the browser compatibility, refer to http://caniuse.com/.