The Rebbe's guidance on guarding one's speech and judging others favorably:
Lashon hara — even when true. Speaking or writing lashon hara about any Jew is forbidden even when it is true, because words have real effect; turn instead to ahavas chinam, especially as the exile nears its end (IK 1173, 1658). Avoid disputes and lashon hara, and put the energy into Torah and mitzvos — peace is the vessel for G-d's blessings (IK 8231). Accusing a rabbi or any Jew of wrongdoing without clear Torah-based proof is a grave sin (IK 3229). Negative stories about Lubavitch usually come from those unfamiliar with it; Ahavas Yisrael forbids repeating them (IK 6942). When the honor of a Jewish woman is concerned, the utmost care is required, and a personal dispute should go to a Rav rather than be discussed further (IK 10549). Don't be swayed by rumors (IK 8250). On the halachic nuances of speech that causes pain, see IK 6932.
Not about oneself either. The prohibition applies even to speaking negatively about oneself; dwelling aloud on one's own faults causes harm, while productive self-assessment leads to growth (IK 1658, 2056, 3795, 4108).
Embarrassing others. Shaming another person, especially in public, cannot be reconciled with the Torah of truth (IK 10636). Criticism during a Torah class should be raised privately, not publicly (IK 7172). Embarrassing someone requires a tikun even after being forgiven (IK 5863).
Speech in education and communal life. Teach students that G-d sees and hears every word — a sign in the classroom can remind them (IK 7569). Those who spread Chassidus bear special responsibility for proper speech, including at farbrengens (IK 6968), and communal decisions call for caution in speech (IK 5866). Improper speech can be among the causes of suffering, to be corrected together with Torah, prayer and mitzvos (IK 2904).
Judging favorably. Judge others favorably while being exacting with oneself (IK 1478), and don't read criticism into silence or an unanswered question (IK 9984). Self-reflection and judging others favorably overcome division and bring unity and blessing (IK 4291, 8695). Yet judging favorably must not lead to harm to the many: only G-d judges alone, so seek others' counsel before acting in public matters (IK 2668).
See also: Personal growth – Refining character: humility, speech and jealousy; Between people – Truthfulness, honesty and constructive criticism; Leadership – Avoiding and resolving disputes; Leadership – Jewish unity and Ahavas Yisrael.