Question:
Is repentance effective if one repents only for some sins?
Answer:
Generally, repentance is understood (and this is also implied by the Rambam) to mean resolving in one's heart not to return to the sin in which one stumbled. However, the Alter Rebbe introduces a novel understanding: repentance is a general acceptance of the yoke of the Kingship of Heaven.
When a person violates even a single commandment, he has, in a general sense, cast off the yoke of the commandments. For the issue is not merely the transgression itself, but what lies behind it-the person's casual attitude to-ward G-d's command, demonstrating that "there is no fear of G-d before his eyes." Therefore, when he repents, his first and foremost task is to accept the yoke anew. Only when a person addresses the underlying cause of the sin can he be confident that he will not return to his old ways.
Never the less, when a Jew returns to G-d and asks Him to forgive him now only for the sins that weigh most heavily upon him, also then, "the Holy One, blessed be He, purifies Israel." Afterwards, G-d helps him, in the spirit of "one mitzvah leads to another," to free himself from all his transgressions, for "one who comes to purify himself is assisted [from Heaven]."
Adapted from Sichat HaShevua