To evaluate the safety of repeated courses of sargramostim ( recombinant granulocyte-macrophage colony-stimulating factor; GM-CSF ) administered subcutaneously to patients with HIV infection and leukopenia. To determine if administration of GM-CSF will prevent some or all of the hematologic toxicity associated with zidovudine ( AZT ) treatment in patients with pre-existing leukopenia. To assess any clinical and/or virologic benefits from administering alternating weeks of GM-CSF and AZT to patients with symptomatic HIV infection who have a history of cytologically confirmed Pneumocystis carinii pneumonia ( PCP ) or a circulating absolute CD4 lymphocyte count less than 200 cells/mm3.