Besides what already mentioned, here's a few more that come to mind...
If top floor, what kind of ceiling insulation -- will it be an oven in summer? If a lower floor, what about noise suppression from people walking and thumping above?
Parking. Most apartments have totally inadequate parking for tenants. There should be at least one space for a studio, TWO (not one) for a one-bedroom, THREE (not one or two) for a two-bedroom apartment. What about guest parking? Street parking is usually not a good option.
Gardening and maintenance. Many landlords/managers will spruce up the building and grounds when there is a vacancy. As soon as the vacancy is filled, the sweeping stops, the plants die, etc.
Laundry room facilities sufficient for the building. Are the machines' timing set so that one cycle is sufficient to do a good job of wash and rinse? The dryer -- do they nickle and dime you so you have to put in more quarters for another cycle to complete drying?
Electrical wiring -- will it handle modern requirements for all the electronics and appliances? At least two outlets per wall, that are "hot" at all times (not wall-switch controlled) is a minimum.
Plumbing. Can the plumbing in each unit be worked on independently without having to shut down the water in the whole building just to replace someone's kitchen faucet?
Sufficient hot water. Circulating hot water, so you get hot water withing a few seconds rather than waiting for a minute or so after turning it on. Minimal pressure drop of the cold water in the shower when flushing the toilet to prevent scalding in the shower.
Can you get good satellite antenna placement for TV in case local cable sucks or broadcast reception now no longer works because it is now digital?
That's it for now, running out of time. I was, in a previous life, an apartment building (income property) appraiser.