(1) Is the floor construction concrete and steel or a wood joist system. The concrete/steel building type is preferred. A caveat is if it is a "loft" style with no ceiling (drywall, etc) and is open to the concrete structure for reasons I'll describe at the end.
(2) Ask if the apartment building was designed to convert to condos at some point. If the potential conversion was known during design, an acoustics professional may have been involved.
(3) Is the space marketed as "luxury?" While dangerous to trust marketing this much, if legitimately so, should have "above norm" acoustical separation between spaces.
(4) Pull a wall plate off a switch that's in a demising wall between units and look for fiberglass in the wall cavity around the edges of the backbox. You may be able to knock on walls and tell if they're hollow or fiberglass filled. If you find two layers of drywall between the plate and backbox, that's a good sign.
(5) Often the bathroom/toilet plumbing is along the corridor wall in newer buildings. Can you hear the water running from the corridor? If so, you can expect to hear the neighbors' plumbing above your unit too. Listen for water hissing in the walls while you run the kitchen sink.
Yes there's noise through walls from adjacent neighbors, but be aware of impact noises above. If floors are hard (not carpet) expect to hear footfall noise unless a resilient underlayment was properly installed in the units and/or the ceiling is isolated in the unit below. If the unit has hardwood floors, check for a gap between the baseboard trim and the floor by running a business card between. If it doesn't fit, then the resilient floor is compromised and your neighbors below are likely to hear your footfalls, and chances are you will hear your neighbors' above too.
[1] https://www.quora.com/When-renting-an-apartment-how-can-I-te...