The Palo Alto specifics
Most of the city's fences are decades-old redwood on irrigated lots — the exact combination that rots posts at the soil line while the boards stay presentable. That split is worth seeing on one object rather than in the abstract: a Palo Alto fence where the posts were replaced and the boards were kept, burn marks and all. One local wrinkle worth checking before work near the back of the lot: fences running through public utility easements need an encroachment permit from Public Works, the one piece of paperwork the city kept.
Heights, corner triangles and the repair-versus-rebuild question across all three cities are set out in the fence rules and permits guide.
Next step
Photograph the worst post at its base and the full fence line showing the lean, and send them through the form — you'll get a repair range before anyone drives out.