In HTML when referencing images, css, javascript, etc... I sometimes use links without the http or https scheme portion, à la. <img src="//www.example.com/dir/file.gif" alt="" />
and I haven't had any browsers choke on it yet (that I know of). I've seen a few other public sites use it as well, but not many.
I even reference the Google jQuery CDN with this syntax on an e-commerce site:
<script src="//ajax.googleapis.com/ajax/.." type="text/javascript"></script>
Obviously, I only do this when I know the server has both http and https capabilities. (Usually my own sites)
So my question is what harm can this cause? What are the pitfalls or downsides?