An apartment inspection is about the boundary
Inside the unit, the tools are the same ones Lou brings to a house: a thermal camera across the exterior walls and windows picks out the temperature anomalies that point to air leakage, missing insulation or moisture worth investigating further; accessible fixtures and appliances are operated, representative receptacles get the tester — and anything that could not be checked is documented; and the unit's own panel — sometimes a sub-panel fed from floors below — gets opened and read.
What cannot be observed matters just as much, and New York's rules make it explicit: systems that could not be reached must be listed in the report as not observed, with the reasons. In a co-op, that list — risers behind walls, the building plant, the roof ten floors up — becomes your question sheet for the managing agent and your attorney — exactly the questions you want answered before you commit.
Related: Manhattan co-ops and condos, explained · What an inspection costs · Schedule an inspection.