The statistical treatment looks solid, good p-values and they even controlled for multiple testing with an adjusted p-value cut-off (alpha) of p < 0.0125
Funding is a bit biased: This work was supported by the National Institute on Drug Abuse (Grants 14118,026002,026104,and 027804 to H.C.B. and Grant 034093 to J.M.G.), the Office of National Drug Control Policy, Counterdrug Technology Assessment Center (Grants DABK39-03-0098 and DABK39-03-C-0098), and the National Institute of Neurological Disorders and Stroke, National Institutes of Health (Grant 052368 to A.J.B.). H.C.B. was also supported by the Warren Wright Adolescent Center at Northwestern Memorial Hospital and Northwestern University, Chicago.J.M.G. was supported by a Harvard Medical School Norman E. Zinberg Fellowship in Addiction Psychiatry Research
Figure 1 has the gist, interestingly, gray matter density slightly increased with Marijuana usage. The changes weren't that extreme for the most part, but statistically significant. The L accumbens has the largest F (Table 2), indicating a larger difference in gray matter density, the other areas don't look that extreme.
I guess no-one can really say what that means exactly - is it good, is it bad? Everything you do seems to change the structure of your brain in some way (like reading a novel [1]), so it's really hard to tell whether this is 'good' or 'bad'.
P.S.: It's a bit annoying that Internet discussions about publications nowadays immediately just scream 'sample size!' without looking at the stats themselves.
[1] http://www.theatlantic.com/education/archive/2014/01/study-r...
MARIJUANA USERS HAVE ABNORMAL BRAIN STRUCTURE AND POOR MEMORY - http://www.northwestern.edu/newscenter/stories/2013/12/marij...
Persistent cannabis users show neuropsychological decline from childhood to midlife - http://www.pnas.org/content/early/2012/08/22/1206820109.abst...
From personal experience, I smoked recreationally from 18 to 24 and definitely felt serious, structural changes in my brain. I won't go into the details since it's anecdotal evidence, but if research like what I linked to and the OP was presented to me, I would have dropped it.
People need to be aware there are consequences to your mental development if you smoke marijuana casually. Obviously the government has blown them way out of proportion, but the problems still exist.
Also while correlation does not imply causation, it does mean 1 of 3 things. Suppose A and B correlate. Let's take a flu medication and getting cured as an example.
1) A causes B (people who take the drug tend to get cured from the flue as a result)
2) B causes A (people who get sick, and heal by themselves tend to take the drug because they feel sick)
3) A and B are both caused by the same thing (can be many things, e.g. the medicine salesman has the flue)
There have been attempts to mathematically define causation as correlation with a time offset (the one that preceeds is the cause, the one coming after is the result). This has had only limited success. That of course does not stop nearly every study outside of the pure sciences from taking such time-delayed-correlations as proof of causation. Are you really suggesting throwing out 99%+ of science over that ?
( and 4. you made a mistake and while it looks like correlation, it's not. E.g. longterm correlations in chaotic variables, like taking the .999999999999999999 correlation between mathematical descriptions of planetary orbits and concluding those planets are actually in those orbits until something large happens [1]. Yes it goes for earth too. The orbit of the earth could alter to throw the earth into the sun, or out of the solar system and there would be little or no warning. There is also no need for "large" events to cause this. Planets' movements do not follow the central limit theorem and therefore cannot be predicted with 100% certainty. The huge problem is of course, that in the real world nearly every problem exhibits chaos, for obvious reasons, not just the stock market)
It should be more interesting to you how reactive you were to the headline of this submission, than to the results.