Almost all websites have HTML errors, even those that appear to display nicely on your browser. Browsers do a pretty good job of being tolerant of errors, but even so, it’s a good idea to make sure your HTML is as perfect as possible, as this increases the chance that your website will display the way you want it to on as many browsers as possible.
I strongly recommend that you use a HTML Validator to check your pages, and my favorite is the W3.org HTML Validator. While it is a little hard to use and unbelievably picky (good!), it’s by far the best I’ve found — and given that it’s written by the folks that define what HTML is, it does the job right.
One thing to be aware of with this tool is that a single error can cause a cascade of error messages, so I typically fix the first error reported, then revalidate. I’ve tested on my site, but I think lots need to be done too… 
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