Minor rendering differences between browser is normal. They come from different manufacturers who optimize to their own design. The page looks fine in all browsers, so minor rendering differences are a non-issue unless you think users are going to visit using multiple browsers and comparing.
Yes, I think it's the classic headache that all novice to intermediate web developers face at some point or another. From my own experiences, traditional HTML (table based) was a complete nightmare for cross-browser compatibility. Since moving over to full CSS, I am learning cleaner coding methods every day and always run a CSS Validator with every new chunk of coding I carry out on any given web page. Of course, this isn't bomb proof, but I notice that rendering issues are very minor in comparison, where a general rule of thumb for myself, is NOT to position text/paras etc, too close to a container edge, that way, you are giving a little "room for movement" ... without compromising your structure on the various browsers people use.