As far as I can tell from the context you give, it refers to cleaning shoes. A "detail" can mean a task that one is assigned to do (especially in the military, though it could be used in other contexts too).
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Avangi Give us a break!
Hi Avangi,
Okay, I apologize a lot. I thought that phrase 'shine detail' has
concrete meaning, so I didn't post additional context. Obviosly I was wrong and I made a mistake. So I apologize again. And thank you for your note 'I've never heard "shine detail" used to describe discussing problems'...That's exactly what