The roof edge, the stair, the cellar, the boiler: four places that tell you most of what you need to know.
Start at the top. Roofs and parapets are where water first gets in, and the edge is where it usually does. Look at the flashing, the coping and the drains. Pooling, patches over patches and loose stone are all honest signs. A roof that has been maintained looks a little boring, and that is the best compliment it can get.
Then the stair. Stairs carry more wear than any other part of a residential building, and they tell you how a place has been treated. Look at the treads, the handrail and the light. A stair that feels safe at night has probably had good care; a stair with a dead bulb and a loose rail usually has a longer story.
Go down to the cellar. This is where a building keeps its records: dampness, efflorescence, patched pipes, old and new wiring in the same conduit. Cellars never lie and they rarely flatter.
Finish with the boiler room. Look at the equipment, certainly, but also at the labels, the logbook and the dates. A tidy boiler room usually means a tidy owner. Add the façade, the windows and the risers, and you have the seven places we always look.