HTML errors and how to correct them

I have recently checked the site I’m in the process of designing (using WP as the CMS; Twenty Twelve child theme) for HTML errors. I used the W3C Markup Validation Service which found multiple HTML errors (75, or something like that).

Many of the errors are omitted tags at the end of paragraphs. I don’t know how or why these errors could have occurred, because I always write my content using the Text editor, and I’d have thought simply hitting the space bar to end a paragraph and begin a new one would not have translated into HTML errors. Shouldn’t the </p> tag have been added automatically in such cases?

So, my question is two-fold:
1. How and why do these types of HTML errors occur when using the WP Text editor?
2. How do I correct these errors? The W3C HTML Validator shows line numbers for each error, but these don’t show up in the Dashboard editor. Then again, neither does most HTML coding. So, a bit baffled as to where to go from here.

Would be appreciative of any advice, pls.

Cheers
Ross