Use the debugging tools supported by the browser. As mentioned above Firebug for Firefox Chrome Developer Tools from Chrome IE Developer for IE.
That way you can detect cross-browser issues. To help reduce the cross-browser issues, use a javascript framework ie jQuery, YUI, moo tools, etc.
Below is a screenshot (javascript-debug.png) of what it looks lime in Firebug.
1) hit 'F12'
2) click the 'Script' tab and 'enable it' (if you are already on your page - hit 'F5' to re-load)
3) next to the 'All' drop down, there will be another dropdown to the right. Select your javascript file from that dropdown.
In the screenshot, I've set a break-point at line 42 by 'left-mouse-click'. This will enable you to break, inspect, watch, etc.
