Certainly, there are questions, but they are resolvable because of the objectivity of morality. Morality certainly involves subjective concerns, but the relevance is other person's subjective concerns, not one's own. The subjective concerns of other persons are objective to oneself. A person has to look at other persons besides himself to determine morality. It's like looking at other automobiles to drive safely.
Introspection is a defining difference between moral and immoral persons.
But in looking back at oneself, one must determine what it is he is doing to other persons. Otherwise, it is selfishness. The Ten Commandments cannot be followed without a concern for other persons. Personal morality cannot be improved except through social morality, because focusing on oneself only creates more selfishness and does not indicate how one relates to others. Of course, subjective reactions are inherent in everything humans do.