The trailing slash itself is not invalid, per se, but it'a very hard for any following markup to be valid unless the element is void.
A particularly nasty one is any attempt to use a supposedly self-closing script tag:
<script src="..." />
This results in the rest of your page being interpreted as code. Oops!
Such slashes were mandatory in XHTML for such elements but aren't a thing in HTML. They're also not invalid, the HTML validator says "Info: Trailing slash on void elements has no effect and interacts badly with unquoted attribute values."