Abdominal upset is among many possible side effects that Atenolol can cause. Other known side effects are dizziness, lightheadedness, drowsiness, tiredness, nausea, vomiting, diarrhea, constipation, etc. Most of the side effects are present only until the body makes used to the drug and then they usually subside.bdominal upset is among many possible side effects that Atenolol can cause. Other known side effects are dizziness, lightheadedness, drowsiness, tiredness, nausea, vomiting, diarrhea, constipation, etc. Most of the side effects are present only until the body makes used to the drug and then they usually subside.