In these studies, the most common omeprazole side effects included: 1  Headaches -- in up to 6.9 percent of people. 2  Abdominal pain (or stomach pain) -- up to 5.2 percent. 3  Diarrhea -- up to 3.7 percent.  Upper respiratory tract infections, such as the common cold -- up to 1.9 1  percent. Dizziness -- up to 1.5 percent.  Constipation -- up to 1.1 percent.