You can easily spot omissions if you take the time to go over your pages when you are finished writing them. Beta test your pages before a large-scale announcement. Also, subject-specific mailing lists are a good way of seeing how well your content and design hold up when examined by subject matter experts. Feed your pages through an HTML checker. Just because it displays correctly doesn't mean that you have clean source.
Most browsers are very forgiving when it comes to missing end tags or quotation marks.
Automated checkers are good for finding the most nitpicky problems in your HTML which could have adverse effects on some browsers. Test your pages on several browsers. Use as many Web browsers on as many platforms as you can and see if there are any glaring formatting problems. For instance, a page that displays perfectly on Netscape may be completely unreadable on a text browser. You should strive to have readable and attractive output on as many different browsers as possible.