It's been quite some time since looking at widgets. Before opening PhpStorm, I was thinking this might be an opportunity to use Views. After opening PhpStorm and reading about WP_Widget::form on the developer documentation site, I quickly saw the return 'noform' was missing in the majority of form() methods in the widgets. These were fixed.
I turned on the preference to check for all the PHPDocs in PhpStorm 2016.3. Most of the classes and constructors in the widget files didn't have comments. A default was put in temporarily with the plan that as I clean up the files then comments can be improved.
Most of my time was spent on the login widget because I couldn't stand the placement of the forgot your password?. This was moved and the Stay logged in was aligned with the Login button.
These changes are now live on Tux Reports.
I didn't play with the Twitter, Facebook, or Google authentications.