Note to people applying for jobs: It's probably not a good idea to say, in your cover letter or resume, that you're unusually attentive to detail.
But if you do say that, make sure that the materials you're providing don't contradict it. For example, your cover letter and resume should be free of typos and cut-and-paste errors. If you're applying for a tech writing or editing job, then the same applies to your writing samples; and your grammar should be impeccable.
But even if you've made no mistakes at all (which is unlikely), explicitly saying that you're detail-focused may lead to some people who look at your application being extra-attentive to details in the materials you provide.
I guess really this is a specific instance of a more general point: If an applicant doesn't claim to be extra-good at something, then I don't expect them to be any better at it than most people. But if they do claim to be extra-good at it, then I'm likely to pay close attention to it.
So if being attentive to detail is an important part of the job you're applying for, and if you're sure that you've been really careful in preparing your application, then sure, go ahead and list "attentive to detail" among your strengths. But if not, steer clear of it.
This is kind of an addendum to my recommendations for applying for tech writer jobs from a couple years ago, but I think it applies more generally than just tech writer jobs.
(But as with all of my posts, I'm speaking only for myself, not my employer.)