We've been logging client-side for a little while now, and while we have tons of log files filled with Facebook like buttons issues, it has been very helpful a number of times.
Of course, some browsers are of course less helpful than others (IE loves "line 0" errors).
Every browser has its quirks on errors. At least IE will give you stack info from window.onerror even without a try/catch, although they didn't get the file name right until IE8. The "line 0" errors are often due to eval scripts where there is no source file, it could even be something like a bad JSON string being passed to a JSON.parse shim.
Of course, some browsers are of course less helpful than others (IE loves "line 0" errors).