Tracking down client side errors will be different depending upon the browser client (and version) because of the varied level of support for debugging provided by the various browsers.
When tracking down an error on the client the first thing you should make sure of is that <debug>true</debug> is included in the client config.
Then for IE the trick is the developer console, which is under the Tools|Developer Console menu or F12.
This is for IE 8 & 9, for IE 7 and earlier it is trickier because you may need to install the Microsoft Office Script Debugger, which adds the required functionality to those browsers (actually I'm not sure about IE 7, it may have the developer console already).
From there you can go to the Script tab and look at the console. Hopefully that will contain more information to help you resolve the issue.
If it doesn't then hitting the "Start Debugging" button or pressing F5 will reload the page and it should then show the errors in the Console.
If it's an error at startup there will usually be two errors listed, the first one is the important error and you can click on the blue link in the error to go to the line that's giving the error which hopefully will provide some sort of clue.
Also, testing Firefox or Chrome will generally produce better error information than IE, so even if you need to use IE it can be useful to test this with FF or Chrome.