And how do we address and prevent them?
Almost anything taken to a ridiculous extreme is bad for you. Problem is, a paleo approach is ridiculously extreme from the SAD-conditioned point of view, so it can be difficult for newcomers to use good judgement about their food choices. While most people see vastly improved function almost immediately, many have made and will make changes to their lifestyle that, while technically within the paleo milieu, still lead them into poor health.
Which health problems are most likely to be encountered by paleo beginners, and what are the most common solutions?
Edited to add: "Fanataicism" was a bad choice of words, as most of the answers seem to be focused on that. Let me try again.
There are a lot of threads on here about some new issue or another that has cropped up since starting paleo. Usually there is a simple fix, but when I see the same problem coming up again and again that tells me there's a problem somewhere, and finding common threads can help us improve, refine and "hack".
Here are some examples:
What have you noticed?
I am Paleo because it maximises my sense of wellbeing and allows me to really enjoy life, and so I take an integrated approach to health and wellness. Therefore I would personally classify social/emotional/psychological issues stemming from overly strict Paleo dogma as health problems (not least because these in turn often have psychosomatic effects with regards to hormones, wound healing e.t.c.). Remember that centenarians almost always come from communities with strong social ties. Obviously those with autoimmune problems e.t.c will find differently.
I think it's very important that we don't alienate people. Food plays a key role in our sense of who we are (e.g. as the focal point of celebrations) and also who we aren't (think about how many ethnic slurs are based on food culture). When I first started Paleo, I didn't really bother to conceal how I felt about what other people were eating - big mistake. By rejecting their food I was implicitly rejecting them.
Discrete compromise is best. For example, everyone is drinking beer, do you:
a) say screw it, I'll have one too
b) join in by opting for a gluten-free alcoholic drink
c) sit in the corner parsimoniously sipping a mineral water, worried that alcohol will lower you food inhibitions
Most importantly, don't let dogma get in the way of n=1. Just by eliminating grains, excess fructose/LA, you are now 85-90% of the way there.
My advice would be to try Whole 30, and if you find that you do well with higher carbs or more fruit or lots of dairy e.t.c then I say you should listen to your body.
Finally, remember that your diet should be something that you can live on and live with - seek out sources of Paleo-friendly food pleasure. Don't just remove foods from your regular diet without searching for delicious new foods to take their place. For example, the first Christmas that I was Paleo, I roasted a goose for the first time for the whole family; I had discovered a delicious new animal (and had supplied myself with pints of tasty fat for cooking in the following months).
EDIT (to add yet another chapter to my monster answer):
As a Paleo beginner, don't rely on your assumptions about Paleo dogma; if you have any doubts, always check. You will spend the first several months researching frantically, but will then be able to settle in to a relaxed pattern, as this new knowledge becomes an effortless part of you everyday life. For example, I mention starting off cooking in goose fat (and also lots of lard and chicken fat). I had assumed that animal fat automatically meant optimal Paleo due to the constant dogma lauding all animal fat, but was later shocked to discover that these fats are relatively high in O6 PUFA, and that I was better off with ghee and beef tallow. (Equally, remember that gluten, MSG and other nasties can often lurk in foods under innocuous names like "vegetable protein". My advice is to print out a list of all their aliases and keep it handy somewhere.)
Also, resist the temptation to over supplement. Starting out, it's easy to find yourself over-eager to optimise, which means that you can allow yourself to be convinced by scanty evidence/end up getting sucked into thinking that more = better when it comes to supplements. Context is key - think interactions (some as yet unknown), depletions, false confidence, money down the drain (literally). When you walk into your local health food store and feel like the proverbial kid in a candy shop, it's time to re-evaluate.
I would have to say the only health problem that could occur from fanaticism is a mental disorder....or eating disorder. This goes to all who constantly ask others....is this or that paleo? If we make the paleo life like raw veganism then there is a major problem. N=1 is the only way to answer the question....is this paleo? Paleo eating can't become a religion like other diets!
Here, for those who think that Paleo is the last word on science, I would quote Mary Midgley (who is a very interesting critic of neo-darwinists like Dawkins):
"human life [is] like an enormous, ill-lit aquarium which we never see fully from above, but only through various small windows unevenly distributed around it. Scientific windows - like historical ones - are just one important set among these. Fish and other strange creatures constantly swim away from particular windows... reappearing where different lighting can make them hard to recognise. Long experience, along with constant dashing around between windows, does give us a good deal of skill in tracking them. But if we refuse to put together the data from different widows, then we can be in real trouble."
Various nutrient-deficiencies are actually possible. While paleo can easily take care of complete nutrition, it takes take paying attention to some things. Grains are actually a source of magnesium and copper and if someone doesn't pay attention and look for good paleo sources of these things then they can actually end up more deficient. Actually the fortification of grains with nutrients, particularly breakfast cereals does some good. It isn't that we want to load up on the Special K, just make sure to cover all of our bases with regards to nutrition. Generally paleo man eat offal, bones and a goodly amount of fibrous vegetation and a diet of isolated fats, muscle meat and some vegetables may not cut it. Supplements are also a viable alternative when it comes to some nutrients like minerals.