During my work on 3DTin, I have learnt couple of techniques that help me debug my WebWorker code.
1. Use postMessage as replacement for console.log
postMessage is how you send some data from the WebWorker thread to the main thread. This is the primary way of returning the result of the computation you perform in WebWorker. But we can use it for other purposes too. Here is how you can use the postMessage mechanism for communicating both the successful response as well as debug messages.
2. Catch exceptions and send their stack trace over postMessage
When an exception occurs in the code running in WebWorker, the debugger will print the line at which exception occurred, but not the entire stack trace. In most cases the whole stack trace can help you find the root cause quickly. To achieve that, place most of your code that runs in the WebWorker inside a try-catch statement. Then in the catch clause extract the stack trace of the exception, format it nicely and send it to the main thread using postMessage, as discussed in the first technique above. Here is the exception handling code that helps you extract stack trace at least on Google Chrome and other Webkit browsers. I have cherry-picked it from the stacktrace.js library. If you need a browser agnostic solution, paste the stacktrace.js library at the beginning of your WebWorker code.
I hope this makes your life easy while debugging WebWorker code.