This is an interesting question, partly because everyone is looking for different information when looking to relocate. For some, seeing a lot of kid's toys and basketball hoops and bikes in a neighborhood is a plus and for some it is a negative. Same for proximity to commute routes, "conveniences" etc. So it is interesting to see what people are honing in on in this discussion.
I suppose everyone cares about crime, but figuring out what kind of crime and how often it is happening is the realistic question. I look at the police blotter in a town I visit regularly, an affluent suburb which seems to have a lot of car thefts and security alarms, maybe because its residents are away at work most of the time. Along the lines of the kitchen knives observation, I have noticed that within my area, there are two chain pharmacies (same chain) and in one, there are a lot of items behind locked plexi and the other has them more accessible. Possible data point for more pilfering in one area? It makes an impression.
The one place I probably get most of my "feel" for a place is the grocery store. How is it maintained, what is the general demeanor of the staff, and what do they stock. There is also a bit of noticing how my own presence is regarded, how noticeable I am in that context. This tells me a lot about the spread of community the store serves, the working conditions for lower wage workers, and something of the investment or pride in the community.
The second thing I notice is what I'll call "noise vectors" - proximity to a fire house or train crossing, flight path for an airport, neighbors with a garage for working on vehicles (revving an engine until 1AM is going to be happening all the time in my
experience) or a pool and "outdoor entertainment area" close to the property line.
All of these impressions go into the gumbo. hopefully you have time to decide at a reasonable pace anyway and can take the time to get comfortable with a decision. But it is one of the scarier aspects of moving because while it's not a blind leap exactly, it's hard to really "know" a place until you've spent some real time there.