When you say "Anaheim", do you just mean the area immediately surrounding the resort, or do you mean the city (do you plan to do much driving around to grocery stores, etc?)
We lived several years just half an hour from Disneyland (and we visit several days per year now that we've moved out of state), and with the exception of the Disneyland side of Harbor Blvd., the surrounding area can look a bit dirty/trashy. okay, some areas can look VERY dirty/trashy!
however, the fact that the area can be very big-city-ish, does not necessarily make it dangerous. we always make runs to different restaurants in the area, or to 31 Flavors, and sometimes even the mexican grocery just beyond the Ball Rd./Harbor Blvd. intersection. granted, not my favorite places to be, but i've never felt like our safety was in jeopardy.
anaheim, like many other southern california cities, has a very large hispanic community. i think when people come from areas that are not populated in this way, and see a lot of hispanic people, they sometimes automatically thing "gangs".
in well over 100 visits to DLR, we've probably encountered many people who were in fact, gang members, but as the other poster said, they were just there celebrating the day with their families. we've never once seen anyone cutting in lines, or fights, or anything like that.
in fact, the worst thing i've ever seen at disneyland was a (caucasion) parent angrily belittling their small child who was afraid to go on the Pinocchio ride! now THAT was distressing!