This custom Behat FeatureContext includes a step called "Then every link should work". It checks every visitable link on a page for a 200 code.

FeatureContext.php

<?php

use Drupal\DrupalExtension\Context\RawDrupalContext;
use Drupal\DrupalExtension\Context\DrupalContext;

use Behat\Behat\Context\Context;
use Behat\Behat\Context\SnippetAcceptingContext;
use Behat\Gherkin\Node\PyStringNode;
use Behat\Gherkin\Node\TableNode;

use Behat\Mink\Exception\UnsupportedDriverActionException;
use Behat\Mink\Exception\ExpectationException;

/**
 * Defines application features from the specific context.
 */
class FeatureContext extends RawDrupalContext implements SnippetAcceptingContext
{

    /**
     * Initializes context.
     *
     * Every scenario gets its own context instance.
     * You can also pass arbitrary arguments to the
     * context constructor through behat.yml.
     */
    public function __construct()
    {
    }


    /**
     * List of URLs we have visited.
     * @var array
     */
    public $visited_links = array();

    /**
     * @Then every link should work
     */
    public function everyLinkShouldWork()
    {

        $elements = $this->getSession()->getPage()->findAll('xpath', '//a/@href');
        $count = count($elements);

        foreach ($elements as $element) {
            // If element or tag is empty...
            if (empty($element->getParent())) {
                continue;
            }

            $href = $element->getParent()->getAttribute('href');

            // Skip if empty
            if (empty($href)) {
                continue;
            }

            // Skip if already visited
            if (isset($this->visited_links[$href])) {
                print "Skipping visited link: $href \n\n";
                continue;
            }

            // Save URL for later to avoid duplicates.
            $this->visited_links[$href] = $href;

            // Skip if an anchor tag
            if (strpos($href, '#') === 0) {
                print "Skipping anchor link: $href \n\n";
                continue;
            }

            // Skip remote links
            if (strpos($href, 'http') === 0) {
                print "Skipping remote link: $href  \n\n";
                continue;
            }

            // Skip mailto links
            if (strpos($href, 'mailto') === 0) {
                print "Skipping remote link: $href  \n\n";
                continue;
            }

            print "Checking Link: " . $href . "\n";

            // Mimics Drupal\DrupalExtension\Context\MinkContext::assertAtPath
            $this->getSession()->visit($this->locatePath($href));

            try {
                $this->getSession()->getStatusCode();
                $this->assertSession()->statusCodeEquals('200');

                print "200 Success \n";
            }
            catch (UnsupportedDriverActionException $e) {
                // Simply continue on, as this driver doesn't support HTTP response codes.
            }
            catch (ExpectationException $e) {
                print "200 Success NOT received \n";
                throw new \Exception("Page at URL $href did not return 200 code.");
            }
            catch (Behat\Mink\Exception\DriverException $e) {
                throw new \Exception($e->getMessage());
            }

            print "\n";

        }

        print "Done! Checked $count Links";
    }
}

Thanks for this. Exactly what I was looking for.