One place that blind spots can be found is in strong reactions. An unusually strong negative or positive reaction or stance may suggest engagement in a process Freud called reaction formation. Reaction formation involves unconsciously transforming an unacceptable or undesirable impulse into its opposite. For example, according to this view, former New York governor Elliot Spitzer's efforts to crack down on prostitution when in office may have been a direct reaction to his own desire for and involvement with prostitutes.
A number of studies have found evidence for reaction formation. In one (Morokoff, 1985), female participants high in sexual guilt deemed erotic imagery to be unacceptable and reported low arousal in response to it. Physiological measures revealed, however, that these same participants actually showed the highest levels of arousal. The same pattern was later found among homophobic men, who were more physiologically aroused by videos depicting homosexual intercourse than were non-homophobic men (Adams, Wright, & Lohr, 1996) - see also Chris Cooper's character in the film American Beauty. This tendency is not confined to sexuality. Harsh judgments of others' behavior may reveal a personal insecurity - for example, that highly ambitious co-worker may especially irritate you because of your own unexpressed ambitions. Blind spots in these cases need not be objectively negative traits, just traits that are experienced as personally shameful or unacceptable.
Just as extreme negative reactions to a trait in others might suggest the presence of that trait in onesself, extremely positive attitudes or behaviors may suggest a lack, or a feared lack, of a desired trait. Research shows that people who want to appear non-prejudiced may go to great lengths to demonstrate their generosity and positive attitudes towards a stigmatized group, especially when their sense of themselves as a non-prejudiced person is threatened (see this paper for a review of research on this topic). Other kinds of overly positive or rigid attitudes may also suggest underlying negativity, ambivalence, or doubt (as in the film with this title).
Another way to find your blind spots is to ask the people closest to you to give your honest, constructive feedback about your strengths and weaknesses. It turns out that when it comes to evaluating our behavior, other people sometimes know us better than we know ourselves (Vazire, 2010 - also see this essay). Asking for feedback can be hard to do, and to make things more complicated, people may not be totally honest for fear of being hurtful (hence the classic "it's not you, it's me" break-up line). On the other hand, loved ones may appreciate the opportunity to air their grievances.
Whether we do it on our own or with the help of others, uncovering blind spots can be a delicate process. An accepting and understanding attitude is likely to make it less painful and more effective.
Baumeister, R., Dale, K., & Sommer, K. (1998). Freudian Defense Mechanisms and Empirical Findings in Modern SocialPsychology: Reaction Formation, Projection, Displacement, Undoing, Isolation, Sublimation, and Denial Journal of Personality, 66 (6), 1081-1124 DOI: 10.1111/1467-6494.00043
Vazire S (2010). Who knows what about a person? The self-other knowledge asymmetry (SOKA) model. Journal of personality and social psychology, 98 (2), 281-300 PMID: 20085401