The first stage of checking a web-site is to make sure that you have valid HTML (or XHTML). This can be done with a HTML validator online or ofline. Your own browser may ignore certain errors, but there is a significant risk that markup errors will result in display problems in some browser or other.
There are sometimes reasons for including invalid HTML. For example some non-standard NOINDEX element, for the benefit of site search engine ranking. But you should only tolerate HTML validation errors if there is a clear need for the non-standard markup, and if you have tested the result in a variety of browsers.
Otherwise there should be no HTML validation errors and should be never, If you site is to work word wide, it should browser independent, with no HTML validation errors. Some online HTML validators are:-