Validation Errors and Warning

Yes, you should clean up those errors. Some errors are not a big deal as they are the result of changing standards or other inconsequential coding things. But many of yours are coding errors that can cause problems — in particular the ones that have to do with missing, open, unclosed or extra tags. Each error tells you where and what the problem is — so you have to go through your code and find them. You also need to validate each page on your site. Yes, it can be a pain but quite necessary if you care about clean coding.

Here is some more info on validating:
http://codex.wordpress.org/Validating_a_Website

On the bullets — yes there is CSS code in the base.css file that eliminates the bullets — here:

ol, ul {
		list-style: none; }

You can stop that behavior by either removing the above code or styling a particular list to have the bullets (or whatever you want there).