Almost all of the new browsers come with developer tools to help locate & debug issues that could be preventing a web page from running as intended in that browser. A good first line of action would be review & resolve the errors & warnings displayed in the Console that is generally part of the browser's native developer tools.
In Firefox, there is an Error Console in the Tools menu.
IE 8 has a Script Console under the Script tab in Developer Tools which is accessible with keyboard shortcut F12.
Safari (on Windows) has the Show Error Console option in the Develop menu.
Opera's Error Console is a tab present in Developer Tools (also called Dragonfly) that is available from the Tools menu under Advanced option.
If this step doesn't help then review these links for tips on addressing specific issues -
- Stack Overflow: What are the typical reasons Javascript developed on Firefox fails on IE?
- Migrate apps from Internet Explorer to Mozilla