(disclaimer, I work with the Dart team)
Luckily, Dart compiles to modern JavaScript, so it will run across modern browsers. You don't need to wait for other browsers to directly adopt Dart. Heck, it's not even in Chrome yet (although you can get a binary build of Chromium+Dart VM for testing).
As for "what exactly is the problem", it really depends on the scope of the project. For very small apps, JavaScript is doing great. Sure, startup performance can be much better (imagine if you had to parse all the C code just to run your browser every time you started it up!), there's no built in libraries/modules, and there are dark alleys to avoid. But, as has been demonstrated, there's a lot of great apps written with JavaScript on the web.
However, we feel the web needs more complex, more performant apps (eg more apps on the size of Google Docs). With user expectations shifting to apps, we feel the web needs to remain competitive to the demands of modern app developers. We'd like to help keep the web a compelling platform for developers from all platforms, like Android, iOS, and .NET. Those developers have a different set of expectations of their tools, languages, and platform. Dart is a project that aims to be a solid choice for developers building more structured web apps.
There are two core tenets to Dart: must be instantly familiar and must compile to sane modern JavaScript. Those are very interesting and challenging design and engineering constraints, but we know and feel they are critical for the web at large.
As for performance, the team feels they can do better than the current crop of JavaScript engines. They should know, they build V8. :) However, it's early days so it remains to be seen how they'll do.
It's very early for the Dart project, and Scirra is off and running. For now, you're definitely right, keep on the JavaScript train. The Dart team is working hard to build a 1.0 of the platform and SDK, but until then it's a good time to let us know what features you need or want.
Hope that helps,
Seth