We currently live in a small town and it is probably to small to see a transitional area, except as mentioned by others, the neighborhoods seem to become less well maintained. We lived in a large city many years ago and it was much more obvious there.
There is, and it is a fairly fluid one. An easy way to track it is the arrival of gang graffiti in neighborhoods and on mailboxes where there was none before. It also seems that cities in general neglect things such as street maintenance in higher poverty areas. There is some obvious contradiction in the transition zones: townhouses or condos surrounded by fences and World War II era homes, elderly residents who cannot afford to move with meticulously maintained homes in the middle of those that are rapidly deteriorating. The crime rate, or at least the pattern of where it occurs, follows this transition zone, though there seems to be a delay.
There are three government housing projects in a town of 20,000. One, especially, is the center of crime while the other two have their share of drugs, shootings, beatings, robberies, etc. The crime rate remains fairly consistent in this one because most of the residents do not work or engage in any kind of productive activities.
We are a small town under 3,000 and there are two apartment complexes. One is specifically for low income rent. The SES of this complex does tie into a little of the ciminality of that area. The other is not specifically for low income, but that is the SES that tends to gravitate there. The fact that there is a higher incidence of criminal activity at these areas relates in part to the higher number of residence in the complex as opposed to neighborhoods where residents are a little more spread out.
There is clearly such an area in my town. The clearest physical sign of disorganization is poorly maintained homes and apartments. You have houses with peeling paint, weedy yards, broken-down cars in the driveways, things like that. (This is a small town of about 20,000 people so we don't have large apartment buildings even in our poorer areas.) This is the area that tends to have the most crime in town, much of which is related to drugs.