The incident left a major stain on the company's history.
There is no blemish on his record.
The scandal left a stain on the company's history.
The incident put a blemish on his career.
He worked hard to wipe away the stain of his past.
欠点 is a neutral defect or shortcoming, while 汚点 carries a stronger sense of shame or damage to one's reputation.
汚れ is a concrete, physical dirtiness, whereas 汚点 is usually an abstract blemish on a record or reputation.
汚点 refers specifically to a stain on one's reputation or record, matching the metaphorical use of 傷 for disgrace.
弱点 refers to a weakness or vulnerable point, while 汚点 refers to a shameful mark or blemish on one's history or reputation.
A Sino-Japanese compound of 汚, associated with dirtiness or defilement, and 点, a point or mark; literally a dirty mark, extended to a figurative blemish or disgrace.