I've now tested more. One thing I noticed is that AO seems to change the relative urls in CSS files e.g.
@font-face {
font-family: 'Mono Social Icons Font';
src: url('fonts/MonoSocialIconsFont-1.10.eot');
to absolute urls. And here it's expended to urls starting with "http" instead of "https" resulting in many warnings for insecure content.
I don't really understand how AO and HTTPS plugins work together and where this could be fixed. As last resort I can always hard-code absolute URLs in my stylesheets but I'd rather not.