Easy!Appointments is based on CodeIgniter and thus can be extended and configured to take advantage of the popular PHP framework. You can easily enable PHP error logging in order to debug your installations and store information into plain files on your server. Read the following guide from the official CodeIgniter manual.
https://ellislab.com/codeigniter/user-guide/general/errors.html
Enable Error Logging in Easy!Appointments
Open the /application/config/config.php file and go to line 201: $config[‘log_threshold’] and change its value to 1. Log files will be stored in the /application/logs directory so make sure that it is writable.