On the spec side, we have access to the the column number and… <drumroll>… the stack trace! This took a long time, but it's in now. https://mikewest.org/2013/08/debugging-runtime-errors-with-w...
Chrome already has support and.. if past release schedules are maintained, all users of Chrome should have this feature within the next week. Firefox already has support for the CORS behavior and is working on adding the stack to onerror.
If you want cross-browser stack traces: https://github.com/occ/TraceKit. It's used reliably by many large projects. If you want to track these in a reasonable dashboard: https://getsentry.com/ Sentry even supports sourcemaps, so you can map an error of "e.a is not a function" back to the original unminified JavaScript. Also, open source.
We're turning on CORS for the Google JS Library CDN, too.