This is kinda my area and I have access to the actual study, so I'll try to deal with a couple specific things that have been noted and then go off on my general complaints.
It's called the Flynn Effect, and wikipedia has a pretty decent write up on it.
They don't show any evidence of brain injury, either.
OK... on to my complaints. First of all, it's a longitudinal study and Omega is right: this isn't an experiment so they can't really make a causal claim, but even the authors of the paper do. They're criminologists, it seems, and not psychologists and frankly I don't know what they're taught is appropriate methodology for making claims of causation from a correlation, but everyone around here knows the chant so I won't dwell on that too much more than to say that there's at least two possible alternative interpretations of the data: The first is stupid people get into more fights, thus increasing their chances of injury. The second is that stupid people are more likely to be "seriously injured" in fights. I'm leaning toward the former.
My second problem with this study is methodological and related to the causal claims... I can't tell for certain from what's presented in the study, but it looks like what they did was take the different "serious injury" groups from the 3rd data collection and compare them to the average from the first data collection, which if there are initial differences in IQ this would conceal them. The better way to do it if they want stronger causal evidence would be subdivide all the data at the beginning by injury group and then compare the changes within groups and then compare to the averages. It would have been easy to do and would have taken care of this question from the start, but I don't see it addressed. This makes me suspicious.
Third, they never define what a "serious injury" is and the data is self-report and even if they did the average IQ difference between one "serious" injury group and the next is extremely small: a 0.2 drop in IQ per serious injury in one year for females and less than a .1 drop for males. Surely physiological differences between males and females account for this, right? Wrong. Social pressures for females not to get into physical altercations are much higher than for males.
Note: OK, I see what they did. They're claiming a 1.62 loss per fight in a year for males and a 3.02 point loss per fight for females. I was looking at data presented at the end on a graph that's in standard deviations from the mean. Fuckers need to learn to label their god-damn y-axis.
Fourth problem. What did they control for? Age, socioeconomic status, race and gender. That's nice of them and all, but I want information on things like playing other contact sports, drug use and skipping school, for example.
So as far as I can tell this study is poorly designed, poorly executed and makes claims that it cannot back up.