I like organizing my report like this:
1) room #, patient name, age/gender, date of admission, isolation precautions, code status, provider group following them.
2) admitting dx; other hospital problems we're treating
3) course of hospitalization (any notable procedures, surgeries, or other hiccups during their length of stay); what happened to the patient today
4) health history
5) assessment data; at bare minimum, I include neuro status (A&O, CVA hx, baseline tremor, etc), CV status (rate, rhythm, BP, heart sounds), pulmonary assessment (lung sounds, chest tubes w/ drainage amount, RA or O2), GI/GU data (diet, fluid restrictions, ACHS, Foley), skin (skin breakdown, wounds, CHG bath) and mobility (independent or level of assistance with ADLs), IV access with running gtt rates, pain assessment/interventions, pertinent lab results
6) plan of care, including possible discharge plans or future procedures/surgeries; for this part, it's helpful to look into the provider's most recent progress notes.
I think the way you arrange your handoff report also depends on the unit you work in. I work in a cardiac PCU, so I ALWAYS include a detailed cardiopulmonary assessment. This setup up isn't perfect, but it works for me - it also helps me see the "bigger picture" as you said.