Welcome to WebmasterWorld, rulive.
Are you're running Explorer for Mac (shudder)? That's an unbelievably obtuse and non-standards-supporting browser. PC people complain about Netscape 4, and Mac people complain about Explorer 5.
My best advice is to validate that Fireworks generated code first. Use the validators at W3C:
HTML Validator [validator.w3.org]
CSS Validator [jigsaw.w3.org]
If you know you have valid code, you've gone a long way to getting it to work cross-browser. And don't believe that auto-generated code is automatically valid. It very often is not.
Even then, the cross-browser problems you describe may be there. Often you need to settle for making sure the page works and give up on making sure it always looks the same.
For this reason alone I would never make a dHTML menu the only way to navigate a site. And then there's the search engine spiders, which you can think of as reltively dumb browsers. If icab can't deal with the code, there's a good chance Googlebot, Slurp et. al. will also be confounded.
In terms of testing for less widely used browsers, I depend on two things:
1.valid code (as above)
2. pages that work on IE6/pc IE5/mac, NN7/pc, Opera7/pc and Safari/mac
We have a hot thread about the value of validating code going right now that may be of value to you: