I've never seen that JS error before, on my site or anyone elses, so there must be something specific to your site.
As for githubs in general ... remember that github is the "bleeding edge" code, where we commit all code changes. Being human, sometimes we screw up. Classic example, on Fri evening we managed to commit a change which caused all empty lists to error out instead of displaying an empty list! And although it obviously got noticed and fixed very quickly, some folk had heart palpitations when their sites suddenly started pitching the dreaded '500 error'. So as Rob says, we strongly recommend you use something like Akeeba, to maintain a 'sandbox' copy of your site, and test github updates before applying them to a live site.
But when it comes to JS errors in the backend which aren't showing up on anyone else's site, the only thing we can do is log in to your site and debug it by hand. Usually these site-specific things come down to some other 3rd party plugin doing something it shouldn't. Or, for instance, yesterday I tracked an issue with backend weirdness down to a "mass quantity, dirt cheap" shared hosting provider restricting concurrent database connections to 2, so our AJAX calls during loading of element admin pages were failing, and pitching seemingly unrelated JS errors on load.
-- hugh
