One impact of shows like "America's Most Wanted" would be to increase awareness of criminal activity and invoke the public's help in being vigilant. The notion of arousing consciousness of the more untidy aspects of society would be one reality or effect of the show. In a more sinister and skeptical light, shows such as this one help to enhance the idea that anyone could be a gumshoe detective or anyone can make a laudable arrest based on information gleaned from "America's Most Wanted." The idea of an "armchair police officer" might be a bit dangerous because of the implications present. At the same time, it should be noted that shows such as this help to enhance fear of crime and the belief that crime is rampant, helping to feed misperceptions.
One important effect is that it opens the the door into the lives and demons of people that, in the outside, look as normal as everyone else. The case of sociopaths is quite strong in AMW, especially when it comes to how they cold-heartedly plan the worst tragedies seen in our country. When molestors are openly exposed, we see how they are also people with whom we would probably trust our children because their scheming ways are so extremely well-executed. To me, it just helps me open my eyes and stop trusting people so much, especially today when everyone is so easily-available to everyone else.
As with all shows about crime, it can have a tendency to reinforce stereotypes people have about what a criminal is. With shows like Cops and this one, they most often tend to film in big cities, or tell stories about crime in big cities, and since cities also tend to have a higher minority population, and minorities tend to earn less on average, we see a disproportionate amount of African-Americans and Latinos on crime shows like this one. That repetitive message, over time, can reinforce stereotypes and prejudices already in existence.
In this particular show, an effect it has on peoples' actions could be that citizens participate in law enforcement. They are on the lookout for the criminals, they phone in tips, they essentially become deputized nationally. Because America's Most Wanted has been so successful at finding difficult to apprehend criminals (cases the police have had limited success with), it also sends a message to society that if you commit crimes, you will be caught, and society will help us catch you. It's a disincentive to commit crimes.