It seems like your quick registration configuration is not correct.

Try double check of my instruction below :

1. Check my attached screenshot below whether you have enabled for those setting from backend
2. Once you have decided to use quick registration form, you have to configure which custom field you would like to show on the quick registration form, you have to modify this from your backend > Easysocial > profile type > select your profile type > custom field > edit the custom field > click view > enabled show in mini registration .
3. You have to set those mandatory custom field for example : full name, username, password, email field.