What is the ruling on one who made a covenant with Allah not to look at a neighbor's house, then broke his covenant, and how can he expiate for his sin?

It is not permissible to look into people's homes without their permission, and this prohibition is particularly emphasized concerning neighbors. It is narrated in the Hadith (definition) that the Prophet, peace and blessings be upon him, said to someone who peered into his house: "If I had known you were looking, I would have poked your eye with it."

Breaking a covenant with Allah Almighty by committing a forbidden act is more severe than other sins, as it combines two transgressions: breaking a covenant and committing a forbidden act. What the questioner observes as the ill effects of the sin is indeed one of its consequences. Therefore, he should thank Allah for repentance and for continuing upon it, and he should increase in supererogatory acts of worship and righteous deeds, and offer expiation for a broken oath. Repentance wipes away what preceded it, and the one who repents from sin is like one who has no sin.