Common issues I have heard of in 2 1/2 years participating in the online paleo community (but not experienced personally):
*Skyrocketing total cholesterol and LDL - jury is still out on long-term effects of super-high cholesterol from eating paleo and high in animal fats.
*Fat soluble vitamin poisoning (or just elevated blood levels of retinol, D) from high consumption through foods combined with supplementation.
*Worsened hypothyroid symptoms (likely from neglecting to find a reliable iodine source after no longer consuming processed foods with lots of iodized salt), or even development of hypothyroid after becoming paleo. Always seen with VLC/ZC (tons of meat)...
*Severe lack of appetite on a VLC diet higher in fat and protein, leading to chronic undereating and often to exhaustion, lack of endurance, and muscle loss.
*Serious exacerbation of OCD and eating disordered tendencies (usually pre-existing) leading to debilitating anxiety and guilt surrounding food, and/or to increasing amounts of self-deprivation (most commonly zero carb and/or 'fasting') which usually causes various serious health side effects (extreme weight loss to emaciation, depression/anxiety, and infertility/amenorrhea being the most common).
*Weight/fat gain due to believing the people who say calories don't matter and eating a high-cal, high-fat diet.
*Disturbed sleep/insomnia. Usually caused by ketosis.
*Constipation or diarrhea/extremely soft stool, or even both alternating. Caused by high protein/no starch.
For lean/thin individuals particularly, who eat low or zero carb though often higher in calories.:
*Muscle wasting, unintended weight loss to extreme/unhealthy levels
*Hormonal imbalances for both sexes, amenorrhea and infertility in women
*Exhaustion and lack of endurance, inability to recover from workouts
*Persistent hypoglycemic issues while in ketosis/eating low carb, no matter how long they try to tough out the 'low-carb flu'. Including low blood pressure/faintness, headaches/migraines, brain fog, slurred speech, irritability and anxiety, etc.
ETA: On a LC diet, thin people seem to experience one of either extreme of appetite: almost no hunger, or rather ravenous hunger which can't be satiated without starch. I've never been hungrier in my life than when I was VLC, but no matter how much I stuffed myself with fat/protein/veggies I never felt satisfied. Add a moderate amount of starch (say a minimum of 50g with my 2 or 3 daily meals) and I am totally satiated. It's literally the opposite effect that overfat people report on LC.