Actually, the same HTML page can look different in different browsers - browsers process the original HTML file and build their own internal representation of the page. So, the only reliable way to make sure that a script will work in several browsers is to run the script with each browser.
In theory, the new Tree model implemented in TestComplete 6, which is currently in the beta stage, should minimize the differences since it reflects the native HTML objects hierarchy. But again, it depends on the browser's implementation, and it is better to try to make sure that your script can work with a browser.
If the information you are working with is static then it shouldn't be a huge problem (other than appearance). I would still use IDs and NAMEs in any of your tags, though. I've been finding that it is much easier to work with web apps when you use a good naming convention.
I am actually testing an ajax application right now, and I've run compatibility testing against Firefox and IE and it has worked for the sections I've set up so far, even though the Firefox appearance is squished.
If the items aren't identified, though, then it is really tough. That is a problem I was having in the beginning of my testing.
Try tossing in a couple of names or ids and see if that helps you to find the object on the page a little easier.
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