A short review of types of moral hypocrisy:

Although individuals might easily recall worthy behavior, unethical incidents might “disappear” from their memory. … Even when people recognize their ethical inconsistencies, there are various ways to redefine unethical behavior as morally acceptable or at least as not entirely unethical. For example, participants can interpret not cheating to the maximum extent as maintaining ethicality or as resisting obvious temptations. … They can reframe taking a newspaper without paying the full price as paying something despite the absence of external enforcement measures. … People may justify their actions by reference to norms (“everyone is doing it”), to external pressures (“if I do not do it, I’ll be fired”), or to altruism and a greater cause (“this is what it takes to ensure people do not lose their jobs”). Other factors attenuating perceived unethical behavior include lack of intent, lack of clear harm, or absence of a concrete victim. … redefinitions, reinterpretations, and justifications allow one’s own small deviations from ethical standards to go unnoticed and give way to gradual relaxation of one’s ethical code and moral criteria.

That is from a paper focused on one particular type:

A recent example of … “the pot calling the kettle black” was the forced resignation of the Massachusetts Institute of Technology (MIT) dean of admissions. The dean, known for her harsh policy toward students who puffed up their credentials or lied on their résumés, had embellished her own credentials when MIT first hired her; she had never received the bachelor’s or master’s degrees she claimed to have. …

Six studies demonstrate … [this] phenomenon. … Recalling an undeniable ethical failure, people experience ethical dissonance between their moral values and their behavioral misconduct. Our findings indicate that to reduce ethical dissonance, individuals use a double-distancing mechanism. Using an overcompensating ethical code, they judge others more harshly and present themselves as more virtuous and ethical (Studies 1, 2, 3). We show this mechanism is exclusive for ethical dissonance and is not triggered by salience of ethicality (Study 4), general sense of personal failure, or ethically neutral cognitive dissonance (Study 5).  …

The distancing response appeared when the ethical misconduct was both undeniable and hidden. Once the wrongdoing was visible and/or once participants could in some way justify it, participants abandoned the distancing solution. ….

Distancing differs from moral hypocrisy in three respects. First, distancing is elicited when solutions of moral hypocrisy such as rationalizations and justifications fail. Second, distancing refers to self-presentation rather than to judgment of the self. Third, in the distancing response a person uses the same — overcompensating — ethical code for judgment of others and for self-presentation. … [Researchers] found that following unethical behavior, people morally disengaged and were more lenient toward cheating. Such leniency resulted from participants’ justifying their own misbehavior as morally appropriate. In our research, participants could not rationalize their ethical misconduct. Thus, instead of showing lenience toward cheating (causing further threat to the self), they had to solve the internal tension with a distancing response and demonstrate stricter (rather than relaxed) criteria.