In this essay, the author calls attention to a little-studied but critical aspect of school system reform: the nontransparent and sometimes illogical ways school districts allocate funds and personnel, especially teachers. Drawing on a series of studies produced by his Center for Reinventing Public Education, the author asserts that mayors who seek to reform their schools need to untangle the tendrils of school district accounting practices, and he warns that mayors who attempt large-scale school reform without first attempting to understand their district's financial and personnel practices do so at their peril. In particular, he discusses four common pitfalls mayors should be aware of: (1) unfunded pensions and retiree health-care costs; (2) salary averages hide real spending; (3) more teachers than classes to teach; and (4) opaque central office spending. The author also provides a list of issues for which mayors should demand independent assessments. (Contains 3 notes.)