I went through the site and made sure caching was disabled (it was before). Nothing else (that I can access easily) is loading JQuery as an option. Modules Anywhere had an option to alter how IT handles caching and I enabled that, and disabled loading JQuery in SCLogin (because re-enabling it made the form not load). The odd-looking form is back, this time with the Login button stretched entirely across the screen.
So, caching is disabled everywhere I can find a setting, loading of JQuery is disabled in SCLogin, and the caching done by Modules Anywhere is handled at the article level (which the tooltip says should help with CSS/JS loading issues).
Here's the JQuery report from JomSocial:
And the list of Joomla! plugins from JomSocial:
I'll admit my expertise is in CSS and a little PHP - JS is a foreign language to me.
EDIT TO ADD: the
Authentication - EMail
plugin is to allow site users to login with either their username or email address.