Even before I get to the professional criticism of Anderson and Bushman’s work, I can find some holes in the conclusions on my own. Bushman cites a joint statement made by the American Academy for Pediatrics, leaving out what looks to me to be a very important part: “We in no way mean to imply that entertainment violence is the sole, or even necessarily the most important factor contributing to youth aggression, anti-social attitudes, and violence. Family breakdown, peer influences, the availability of weapons, and numerous other factors may all contribute to these problems. Nor are we advocating restrictions on creative activity.”
Here’s Anderson admitting to the limitations of his work to account for confounding variables: “However, none of these studies can rule out the possibility that key variables such as excitement, difficulty, or enjoyment 
created the observed increase in aggression. In our experience with video games and in the movie literature (Bushman, 1995), violent materials tend to be more exciting than nonviolent materials, so the observed effects could have been the result of higher excitement levels induced by the violent games.”
Sometimes they demonstrate facepalm-inducing ignorance as to how certain games work. “For example, Carnagey and Anderson (2005) found that when a car racing game rewarded players for violent acts, those players were more likely to attack an opponent than when the same game punished players for aggression.” What? Players got a bigger kick out of spitefully blowing stuff up in a race as opposed to getting punished for such behavior? Christ, Mario Kart is poisoning our minds!
Look, if it were just the pundits and politicians who were unfairly cherry-picking Anderson and Bushman’s work and ignoring these qualifiers, that would be understandable. But if that’s the case, then Anderson and Bushman don’t really seem to try to correct the rhetoric for the record, and clarify exactly what their studies are really saying. They don’t seem to object when they are quoted without any attention paid to the limitations of their work, and the necessary cautiousness when drawing conclusions.
Dr. Ferguson and company are pretty aggressive, for lack of a better word, in criticism of Anderson and Bushman’s work. He attacks their methodology, conclusions, and the General Aggression Model, the psychology paradigm that is the very foundation of Anderson’s work. Most of the criticism about the experimental work 
about Anderson and the like is about confounding variables. For example, here’s a whole paper Ferguson likes to cite about how games selected for experiments were compared for violence, but not for competitiveness and pace of action, and how experimental results hinge on a test that has “competitive” in its very name.
Ferguson has published studies that are procedurally similar to those of Anderson and Bushman, but take a different tact in applying analysis. Ferguson notes that Anderson and Bushman’s use of the Competitive Reaction Time test failed to specify which behaviors were considered more “aggressive” – volume, duration, reaction time before a certain cutoff, or some average of these dependent variables – so his own tests standardizes for a two specific behaviors (volume and duration). He thinks their statistical analysis of their results is faulty, and argues that a better analysis of their own results supports different conclusions. Ferguson also relies more than Anderson and Bushman on surveys to collect data from large sample groups about their lifestyles and histories, including their experience with video games.
I will totally concede to skepticism about the reliability of surveys, since the results depend on subjective interpretation of the respondents. After wading through psychology paper after psychology paper, I’ve learned that psychologists understand that skepticism as well, and so the surveys used tend to be of some standardized design with sited research backing up the validity of the method itself. At some points, I just have to trust the experts, and this is one of those points. If Ferguson holds up a particular survey as being a pretty good measure of subjects’ video game experience, aggressive personality, history of violent upbringing (remember this one), preference for violent media, etc., then I have to go with it.