[EDIT: I've sold Muscula years ago and it is now a paid service]
You have to tak a lot of things into account when building your own solution.
For example you will see a lot of noise generated by JavaScript errors in plugins, 10-20% of all errors logged.
Grouping the errors intelligently is an extremely hard problem, because of the very different error messages you get for different browsers and versions.
Also you don't want to log 1,000 errors pr user if you have an error in a mousemove event.
And there is a ton of other stuff to consider.
We've build a SaaS solution like the one you ask for Muscula. We're in private beta at the moment, but working very hard to release. We've already monitored more than 100 million pageviews for JavaScript errors, and we log more than 1 million JavaScript errors a week. And beyound the issues I mention above we also have tackled the problem of displaying errors in minified JavaScript as pretty printed, integration with Goggle Analytics and much much more.
You install Muscula like Google Analytics, just copy a script to your page, and you are logging JavaScript errors.