Yarick

This plugin notifies user if browser check failed. Available checks:
<ul>
<li>Browser version (Chrome, Firefox, Safari, Opera, IE)</li>
<li>JavaScript enable</li>
<li>Cookie enable (require JavaScript)</li>
<li>Adobe Flash Player version (require JavaScript)</li>
</ul>
You can select style for notice. Or disable plugin CSS and write own.
User can close notice to time you set in minutes. It use cookie. You can disable close button.
Also you may set next check time in days. When check is successful.
Browser Check may be integrated with theme. Just place this code: “do_action(‘browser_check’)” in your theme. And disable plugin css from “Settings -> Browser Check” page and write own css for best look in your theme.
Supported languages
<ul>
<li>English</li>
<li>Russian</li>
</ul>

Browser Check

Check browser version, JavaScript, Cookie, Adobe Flash Player version. Warn user if old.

Japh

A supplement to the Theme-Check plugin that adds checks for ThemeForest’s WordPress Theme Submission Requirements, and removes checks that aren’t relevant in that context.
The <a href="https://wordpress.org/plugins/theme-check/" rel="ugc">Theme-Check</a> plugin is required for this plugin to work.

ThemeForest-Check

it helps a lot to discover problems in your theme. It's a perfect tool that everyone who is developing a theme for themeforest should have. Great!

very useful

A supplement to the Theme-Check plugin that adds checks for ThemeForest's WordPress Theme Submission Requirements.

Browser Check vs ThemeForest-Check