The engineers have begun to add Developer Tools support with Dart, which starts to tell the debugging story. With a very recent build of Dartium (2012-01-24) you can try this for yourself. I found breakpoints are working, with a few caveats (eg not working with function callbacks yet.)
To see Chromium + Dart + Dev tools + breakpoints in action:
Dart is getting ready, please do try it out by learning more, browsing the API, using the Editor, or downloading the SDK. I also have a series of posts on Dart. Please let us know what you think!