I was watching this for the 100th time (or it seems like that) with my 10 year old. She turns to me asks "Where did they get all that information from? They can't ask the kids. Where did they get the pictures of the kids awake and smiling? They can't touch human stuff in case the kid touched it and kids are toxic."
I take it that you have not purchased the DVD or Blu-Ray yet. That particular issue is addressed via one of the deleted scenes, a rough-animated clip called "Recon", which was to have been the opening scene of the movie, but was dropped in favor of that scene with Mike's class field trip. Anyway, there are tiny monsters(REALLY tiny, insect-sized), which can fly, and they are employed to take tiny little cameras into kids' rooms and homes and use those cameras to record data, which they bring back to the Monster World. In the animated clip, "Recon", the flying monsters were students at MU, presumably training for a job at one of the big utilities companies like Monsters, Inc. They take pictures of the kid, the layout of the kid's room, proximity of parents' or older siblings' rooms, the walls of the room, etc., and data about that kid is extrapolated from the photos. Because the Recon monsters are tiny, the kids see the camera flash and think it's a harmless firefly, allowing the monsters plenty of time to take pictures. Sometimes, they make mistakes in analyzing what they see in the photos, though. For instance, the kid in the rough animated scene had lots of posters of snakes and other reptiles on his wall, which the monsters incorrectly interpreted as meaning that the kid was afraid of those animals, when we know that us humans put up pictures of things we LIKE, rather than things that scare us. If you pay close attention to MI, Boo's profile had her listed as a BOY, aged four, but they DID accurately describe HER as being afraid of snakes and reptiles, which is why Randall was assigned to be her Scarer, so the reports are kinda hit and miss.