"I've just enabled HTTPS site-wide on my website, lovinity.org"

By making the base URL in info.php https://?

You later say, "In a page where HTTPS is enabled", so I wonder if you changed the base URL, or just checked off all pages as HTTPS.

Do you have a URL on your live site to reproduce the problem?

I have created a demo page at https://lovinity.org/pg/000test for you with the block in progress.

And no, I read about base URL changing making Composr not work, so I'm using the HTTPS setting and I have all pages check marked.

EDIT: Also, in case you're wondering why I'm using HTTPS everywhere, apparently if I want Arrowchat to use HTTPS all the time, every page that it runs on also has to be HTTPS.

UPDATE: Something random happened and it fixed itself XD . It's working fine and serving on HTTPS now.

My only other concern is that the jwplayer serves its logo watermark over HTTP... so if you go to play a video or audio using it, you'll get a mixed content warning.

Thanks.

To fix jwplayer, if it is in HTML5, change "http://l.longtailvideo.com/html5/" to "https://l.longtailvideo.com/html5/" in the JAVASCRIPT_JWPLAYER.tpl template. I just checked it works and we'll make this an official change. I can't fix it for the Flash version (assuming it fails in that version - I did not check), as that's tied up inside the .swf file.

Your other problem would need fixing with a deep change to block caching:
http://compo.sr/tracker/view.php?id=2002
Just clearing the block cache would have fixed, or triggering something that clears it, or waiting out. So long as you don't use the block on both SSL and non-SSL pages you'll be fine.