I know what you're getting at--the question could also be framed, "Now that I eat a strict Paleo diet what am I likely to die from?"
-I would still consider cancer your top threat, even though you eat this diet. It's optimal to start the diet when you're in your mother's stomach, so if you lived the standard American life for 30 years that could cause problems down the road. I suggest you get the acid/base balance right, maybe implement occasional intermittent fasting, and stay away from blood sugar spiking tropical and dried fruits.
-Somebody mentioned bone breaks from falls. I somewhat disagree if you're eating the right acid/base balance, getting enough vitamin D from the sun, eat enough magnesium rich foods, and get the important vitamin K2 MK4. The last could be a lifesaver, but I don't see it recommended enough by Cordain, Robb Wolf, et al very much. Moreso from the Weston Price Foundation.
-Accidents are a big issue. Bicycle travel has the most deaths per km traveled, and then it's motorcycle use. The safest thing to do in the USA is to take a bus or train. If you have to drive a car, it's probably best not to drive a compact car. Go for safety features, defensively drive, keep your cool on the road.
-If you look at overall causes of death you don't see Alzheimers and dementia reaching as high as their incidence. Don't quote me but I've read 1 in 2 people have one of those diseases by 80. They "live" with those diseases, but I wouldn't call it much of a life. There's some evidence that Alzheimers might be affected by a high glycemic index and glycemic load diet. I would also avoid antiperspirants and cooking with aluminum cookware and foil. Not sure but I've heard Teflon isn't the greatest either. Maybe somebody can chime in on this one, but I don't think the causes of these two diseases are fully understood.