We've been using Dart for years on a successful web app, front-end, back-end, and tooling. It's simple to learn. We've had devs experienced in C++ contributing to the codebase in a couple of days without any prior exposure. It's a great general purpose language, and with recent addition of extension methods and NNBD coming soon, it's getting even better. Ecosystem isn't as extensive as JS world, but it's pretty good. (As someone else in this thread stated, I too dislike the required semicolons, but no biggie, and there's an issue to perhaps remove or make them optional, maybe it'll happen eventually)
Give the language tour a quick look: https://dart.dev/guides/language/language-tour
I've been using Dart since the start (~8 years ago), and follow language development very closely.
Let me know if you have any more questions.