There are definitely a lot of issues to overcome when logging errors from a javascript client (as pointed out in the comments to this post). Regardless, the information you can get from it can be really helpful and you should be doing it.
One of the problems we find with js errors is that they don't contain a lot of information by themselves, especially when you're just trapping window.onerror() with minified source. We like to augment the client-side errors with server-side errors/activity as well. If your logging solution supports being able to track errors and activity by a session (username, ip address, etc) you will have a much better time tracking down what caused a specific js error. Putting all the pieces together gives a much better picture.
Try a logging solution that enables you to track more. I run loggr.net, so I am partial to that, but there are other good solutions out there like newrelic.com, loggly.com.