Does eating (or not eating) animals have health implications?

At the request of Jim the Directrix, who has been discussing various issues of diets that don't include animal flesh in comments on "Temple Grandin's rationale for eating animals," I'm here opening a discussion on diet from the point of view of health (rather than of morality).
    It starts with an interchange begun on the Grandin post having to do with vitamin B12. Ken had commented:

Felt an obligation to do some extra research on the vitamin B12 question. I was mistaken to write that its absence would quickly cause a problem. However, predicting the point at which a problem will arise is difficult. It can be less or more than 3 years, depending on genetic factors, how much is secreted daily, and how much is absorbed. It varies from person to person. The danger is greater in a vegetarian family because the onset of vitamin B12 deficiency in children is much faster.

Jim the Directrix replied in an email directly to Ken and me:

Thanks for your response and especially for looking more into the B12 issue. Pundits for eating meat have blown the B12 issue way out of proportion to defend their position. Listening to these pundits gives the false impression that vegans are a great risk of B12 deficiency. Here's what my guru Dr. John McDougall says about the issue:

Vitamin B12 Deficiency—the Meat-eaters’ Last Stand
    Defending eating habits seems to be a primal instinct for people. These days Westerners are running out of excuses for their gluttony. Well-read people no longer believe meat is necessary to meet our protein needs or that milk is the favored source of calcium. With the crumbling of these two time-honored battle fronts, the vitamin B12 issue has become the trendy topic whenever a strict vegetarian (vegan) diet is discussed. Since the usual dietary source of vitamin B12 for omnivores is the flesh of other animals, the obvious conclusion is that those who choose to avoid eating meat are destined to become B12 deficient. There is a grain of truth in this concern, but in reality an otherwise healthy strict vegetarian’s risk of developing a disease from B12 deficiency by following a sensible diet is extremely rare—less than one chance in a million." complete article

Thanks, Ken and Jim, for getting this discussion started. I hope the neutral title I've given it meets with your approval.
    I'll return in a separate post to the question of the morality of eating animals.