Note: This discussion of the positives and negatives of the Paleolithic or "Caveman" Diet is apart from those of lower carb diets in general. People whose bodies are suited to low carb eating tend to feel better on them, be less hungry, and have positive health responses (lower triglycerides and blood glucose; lower blood pressure, higher HDL, among others).
Positives of the Paleolithic Diet
Nutritious - Since it lacks today's processed foods which are relatively "nutritionally empty", there is no doubt that this diet has a high nutrient density. In most cases it will far exceed the minimum requirements for vitamins and minerals, although individual choices could influence this. (For example, see note below on calcium.)
Simple - No counting, no measuring. You eat from the food lists, and that is that.
Emphasis on Physical Activity - Increasing activity levels is seen to be an integral part of the Paleolithic Plan.
Negatives of the Paleolithic Diet
Requires Huge Adjustment - Even more than most low carb diets, eating this way would almost certainly require an enormous change in eating. However much we are told to "shop the perimeter of the grocery store" (which is where the foods for this diet primarily are found), few of us actually stay there.
There is still quite a debate about what constitutes a "proper" paleo diet, and practitioners get quite touchy about it. Still, there is more overlap than not among the various authors. One point that has been brought up is that clearly there are groups of people who have made a genetic adaptation to eating milk and other dairy products those people should go ahead and eat them.
Can be expensive - Grass fed beef, for example, can be hard to find in some places, and almost always costs quite a bit more.
Not much guidance for individual adjustments - Although most do say to stay away from dried fruit or high sugar fruits if trying to lose weight, for the most part the assumption is that just eating from the food lists is good for everyone. Therefore, it will take experimenting for each person to find what works for them.
A Note on Calcium - A frequently asked question about this diet is how a person gets enough calcium without dairy. I would point out that most of the world's population can't eat dairy products and get along just fine. Greens have quite a lot of calcium.