Everyone should care because the biases that are "close to home" are ones that matter. This is an important subject.
Everyone should care
Normative versus descriptive. Saying "everyone should care" doesn't change the fact that some don't, and that for those people, a tidier presentation may help, even if it wouldn't make a difference for an ideal rationalist.
I read an extract of (Wimsatt 1980) [1] which includes a list of common biases in reductionist research. I suppose most of us are reductionists most of the time, so these may be worth looking at.
This is not an attack on reductionism! If you think reductionism is too sacred for such treatment, you've got a bigger problem than anything on this list.
Here's Wimsatt's list, with some additions from the parts of his 2007 book Re-engineering Philosophy for Limited Beings that I can see on Google books. His lists often lack specific examples, so I came up with my own examples and inserted them in [brackets].
[1]. William Wimsatt (1980). Reductionist research strategies and their biases in the units of selection controversy. In T. Nickles, ed., Scientific Discovery: Case Studies, Dordrecht: Reidel, p. 213-259.
[2]. R. Levins (1966). The strategy of model building in population biology. American Scientist, 54:421-431.
[3]. Rudolf Raff (1996). The Shape of Life: Genes, Development, and the Evolution of Animal Form. Chicago: U of Chicago Press.
[4]. They let you use multiple GO tags, and put multiple names within a protein's name field if separated by slashes, but these are not adequate solutions.