I went in and manually installed the following files that did not, for whatever reason, install when I manually uploaded and unzipped the full installer package:
JoomlaFolder/administrator/components/com_easyblog/includes/blocks/handlers/alerts.php
JoomlaFolder/components/com_easyblog/themes/wireframe/composer/blocks/handlers/alerts/fieldset.php
JoomlaFolder/components/com_easyblog/themes/wireframe/composer/blocks/handlers/alerts/html.php

this corrected the problem, except that a new post will not show up in my latest posts module (probably a separate problem).

So it's fair to say that the auto installer isn't the problem, but something is creating this issue for many whenever there's an update.

Hello Irwin,

Thank you for reaching out to us and I apologise for the delay of this response as its a weekend for us now

By the way, I believe your issue with 'call to member function' error is now resolved.

As for your issue where your posts are not displayed in 'latest posts module', can you provide us your Joomla admin access so that we can further check this issue on your site?

Please advise.