From introspection, I've found some ugly inconsistencies in my extension of concern for certain beings and I think that self-awareness can be extremely useful, maybe essential, in improving our moral flaws.
At times, I've found myself having differential concern for certain beings based on their appearance. A good thought experiment which demonstrates what I mean is the following: Imagine a cute puppy (for some help, see the below image)
Now, let's assume both creatures can feel pain and suffer. If you imagine both beings in pain, I expect there's a stronger emotional reaction for the puppy. I think this tendency for the mind to have differing responses to the suffering of creatures based on morally irrelevant traits (like appearance) can have pernicious effects in everyday life.
However, if we can bring an awareness to these tendencies and stay on the look out for more of the human mind's moral inconsistencies, I think there's tremendous room for improvement and growth.