I'm not sure about syntax errors but it is possible to catch js errors using window.onerror event. Searching for "logging errors in javascript" in google gives you a lot of results...
Logging JavaScript Errors To ASP.NET: http://james.newtonking.com/archive/2006/05/02/Logging-JavaScript-Errors-To-ASP.NET.aspx (Unfortunately the link to download in the post is broken).
Logging Client Side JavaScript Errors to the Server: http://www.codeproject.com/KB/ajax/logclientsidejserrors2srv.aspx
JavaScript Error Notifications: http://www.thecodepage.com/post/JavaScript-Error-Notifications.aspx
