You need to establish a strategy for how compatible you need to be. Here are some questions you need to think about and consider their relative importance.
Are you in control of browser deployment to the target desktop systems? This is likely in an intranet situation. If it is true, then you can use all of the features of the browser your deploy, including platform -pecific and version-specific capabilities. You may need to co-ordinate content upgrades with browser upgrades though.
Can you sacrifice old-browser users? If you can get some meaningful statistics of your readership, you may find that only a few percent have an old browser. Are you prepared to support all users or can you disregard some? You need to set a threshold, say 5%, and work out a sub-set of browsers that you will support and from that derive a functionality profile that your must enforce in your design department.
Must you guarantee to work on all browsers of every vintage? In which case, you could consider the lowest common denominator approach and only use those capabilities that are supported by your choice of target browsers.
Do you think you need to only support the latest version of a browser? Users are generally keen to upgrade if it is well worth their while. They likely may not consider your site a compelling reason to upgrade though.
Are you hardwired to a very specific platform/browser combination? Some sites only work on MSIE running on Windows. This is very frustrating for Netscape users or people using any web browser on other non-Windows platforms. Things change and you cannot rely on Microsoft Windows always being the dominant platform. This could change within the hardware replacement cycle type that large corporations like to implement. That might be between 2 and 4 years. If your site only works on a single platform, your traffic may go down as that platform loses market share.
Do you just not care about it? If your page breaks on someone's browser, so what? Maybe it's not important at all. However, don't expect that user to come back - ever. If the script fails to draw some cute animation or change a color the effect is likely to be cosmetic anyway and may not even be noticed. Maybe it fails fairly gracefully if you are lucky.