You can check your web-site using W3C Markup Validation:
The W3C Markup Validation Service
Just put your web-site URL in "Validate by URL" part and it gives you all the errors. It will also give you some tips on how to fix the error.
Usually a web-site maybe broken in some browsers because of the markup errors, but sometimes it's the way the browser renders some tags. Try also installing other browsers on your computer and verify it.
BTW,
A List Apart: A List Apart is a good resource on how to solve browser incompatibilities, try read all the articles.