It's really just better to keep a closing p tag, so you don't have to care about consequence when you edit that part later...
Does not type </p> save anything? No.
<p>
It naturally acts as a clean way to segment
paragraphs of text
<p>
And most of the tag-closing rules are roughly
matched with the rules of using p tags altogether.
<p>
e.g. you can't have a div within a paragraph, so
closing or not closing, divs can only come after
paragraphs!.I just took a sample page out of here which has bunch of p tags open and closed, gzipped the original and the one with </p> stripped, difference was 39 bytes.