If your only goal is creating a book for Kindle, you can ignore validation as long as you get the desired results.
But if you want an ePub book, then yes, you should care about validation, and you must include the closing tag, or make the tag self-closing:
<p class="spacer" />
but some readers might ignore empty paragraphs, so you can add some blank stuff:
<p class="spacer"> </p>
Instead of line-space, you could try reducing font-size.