A recent and oft-cited scientific literature survey concludes (from the abstract):
The adverse effects associated with long-term high protein/high meat intake in humans were (a) disorders of bone and calcium homeostasis, (b) disorders of renal function, (c) increased cancer risk, (d) disorders of liver function, and (e) precipitated progression of coronary artery disease.
a) includes heightened risk of osteoporosis, b) means malfunctioning kidneys and quicker dehydration, e) means heightened risk of a heart attack. Metabolizing proteins for lack of carbohydrates also causes bad breath.