Acoustic cameras like from Noiseless Acoustics are on the market though they seem to be marketed to industrial customers. There are similar mapping systems using a scanning mic like from Soft dB.
It's sensitive enough to noise that I can pick up (and locate) the air vents in a room, even when the sound is at the threshold of hearing. Noise (pink and white), and even more so MLS (maximum length sequence) really "jumps out" (it's very obvious), well below my threshold of hearing.
There's so many interesting areas of research I've never had the time/money to fully investigate. I'd love to play with an "active" system, not just "passive", with a goal of experimentally finding modes of resonance of objects in a room.
I bet once can tell the relative contribution to noise of one physical object over another, but I don't know enough about construction to know if one would be able to separate the door frame from the perimeter gasketing. You do need line of sight for it to work. At the least, you'd have a way to quantify the sound leak, with numbers and reproducibility.
FWIW the Noiseless Acoustics camera costs ~$18k(!)
After setting up the array, once could answer questions like "where is that darn squeak coming from!", and even characterize the undesirable noise, both spatially and spectrally. You could also measure how effective noise isolation materials are, but I don't see what the spatial information gets you.
However, if weaknesses due to "perimeter gasketing, frame, door leaf, or wall construction" result in some sort of localized noise, then a system like this would certainly pinpoint it.