We work on detail orientedness by encouraging DS to slow down and check work. Sometimes being forced to read the problem aloud helps him see his own thinking mistake (obviously this is better for homework than for in-school testing).
Logic puzzles are good for practicing this, especially ones that require inference to understand the clues-- they do have to read the clues several times to find all the relevant information. This slows them down and forces them to consider all the information before coming to a conclusion.
There's also a perspective-taking component to this; how is her perspective-taking generally? If you find situations where she's misreading people's intent, she may need a reasonable explanation that helps her see what's in other people's heads ("Oh, when people ask X, they're generally wanting to know [this particular kind of information]") Can you get the questions and do an "autopsy" on where her perception goes astray, and practice with her understanding what's meant?
I do think both the detail-orientation and the perspective-taking are teachable skills, though it will probably require a lot of commitment to get these skills generalized to all situations.
DeeDee