1. What does it mean?
흐린눈, also written 흐린 눈, pictures intentionally blurring your view. Online it describes choosing not to focus on an inconsistency, embarrassing moment, or flaw, often so you can continue enjoying something.
Also written or said as 흐린 눈, heurinnun
2. The nuance
It can be self-aware humor about a tiny imperfection or criticism of ignoring a serious problem. Those are different stakes; the phrase does not make harmful behavior acceptable.
3. Examples
“소품에 찍힌 가격표는 흐린눈하고 드라마 봤어.”
I overlooked the price tag left on the prop and kept watching the drama.
“좋아하는 작품이어도 큰 오류까지 흐린눈하긴 어렵지.”
Even with a work I like, it's hard to overlook a major error.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.