The argument against farmed fish is that they're fed corn, so you're getting high levels of omega-6, which causes inflammation and ultimately brain damage.
The argument against gluten is that it similarly causes inflammation, which causes brain damage.
For what it's worth, Andrew Weil has an anti-inflammatory diet on his website:
I've seen multiple studies that suggest a correlation between very high Omega-6 to Omega-3 ratios and various cancers, but I've never seen anything regarding brain damage.
Some casual googling just now suggests to me that this notion of generalized "inflammation" and it causing brain damage isn't rooted in an understanding of how pathology works and seems mostly talked about in rather quacky "woo" circles.[1][2]
That being said, it does seem like over-expression of inflammatory mediators like cyclooxygenase-2 (COX2) in the brain can cause brain inflammation[3], and Wikipedia says high Omega-6 to Omega-3 ratio can result in over-expression of COX2 in some parts of the body, so it's certainly possible that high Omega-6 levels could result in over-expression of COX2 in the brain, but I haven't yet seen anything supporting that.
Regarding Dr. Weil, he seems all over the lot with what he advocates. Sometimes he advocates quackery based on "some religious group somewhere says it works," but other times he points to a small body of positive evidence and rightly points out that there's an unfortunate lack of further higher quality research, and other times he espouses very logical or well-supported ideas. And unfortunately, he often doesn't make clear which category the current thing he's talking about falls under and often doesn't cite sources.
For what it's worth, his food pyramid doesn't ban gluten, and explicitly allows for occasional pasta. According to your link, his main criticism of glutenous foods has nothing to do with gluten but that such foods usually contain wheat flour, which has a high glycemic index, even in the form of whole wheat flour. In fact, he strongly recommends low-GI whole grains, including bulgur wheat.
