PathProcessorEntityResourceBC Class not found error after updating to Drupal 8.4
I have fixed the error by replacing the 'core' directory with the latest 8.4.0 version. I then checked the git log and differences which were found in these files:

modified:   core/scripts/drupal.sh
modified:   core/scripts/password-hash.sh
modified:   core/scripts/rebuild_token_calculator.sh
modified:   core/scripts/run-tests.sh
modified:   core/scripts/update-countries.sh


The differences were similar for each file, for example:

--git a/core/scripts/update-countries.sh b/core/scripts/update-countries.sh


I'm not sure exactly how and why this fixed the missing class, but it seems like I have some differences between the 2 versions of the site. 

I then added the changes into git on a new branch and after switching between the 2 branches I don't get the fatal error any more (with or without the updated files). 

It's possible that something was cached and as my site and drush was broken I was unable to clear the cache, refreshing the core files must have fixed it.