JS Error Logs module
The module works exceedingly simply: you just install the module and it gets to work! You can pop back to the module from time to time to see what errors have been logged.
It's compatible with Firefox and IE (all versions, I think...) and recent versions of Chrome. At time of writing, Safari doesn't support it, but it'll be getting in there soon enough. If you're using an unsupported browsers, nothing will get logged when an error occurs.
For developers that are curious, the module works by attaching a snippet of Ajax to the window.onerror event, which sends details of the error to the module to log in a table. Oddly enough, even though window.onerror has been part of the JS spec since the late 17th century, it was omitted from numerous JS engine implementations.