"unimportant detail" is a perfectly correct and usable phrase in written English.
It can be used in a sentence whenever you want to emphasize that a specific detail is not important or not relevant. For example, you could say "The unimportant detail was quickly forgotten and the conversation moved on."
Tate's ironic version stages his murder at the hands of an unimportant detail — a typical detail from a Tate poem, whose work is filled with such effluvia.
I looked at the transcript of it again today and I took a few phrases from it: "When it comes to art, money is an unimportant detail".
When he's off on one of these hyperfocused sprees, there's no such thing as an unimportant detail; his intensity spreads out in all directions, throwing every feature of the scene into equally high relief.
The snap buckles that hold the bag closed are protected with some soft touch plastic, which seems like a tiny unimportant detail but it could actually prove quite useful.
It's an unimportant detail but he's had three wives... What is important is that his followers were there as he lied, but no matter what the evidence they don't believe it".
He recognized early on that visionary photographers could "push their optical equipment to strange extremes, not to reveal unimportant detail, nor as a mere technical stunt, but because the result is beautiful.
-- and he often seems bogged down, as the administrator Davis was, by innumerable unimportant details.
Like true upper-management types, we shy away from those unimportant details.
Make your story vivid but don't get bogged down in unimportant details.
Tiny and often unimportant details, a sound, a colour, a pattern, will be recalled while crucial ones are hazy.
It's a shorthand to keep you from getting all bound up in unimportant details and missing some deeper point.
