The most common side effects of Zocor are headache, upper respiratory infection, nausea, constipation, stomach pain, dizziness, eczema, diabetes, trouble sleeping, muscle pain, abnormal liver function tests, urinary tract infection, swelling, and problems with thinking and memory. Zocor can cause some serious side effects, too. Before taking Zocor, talk to your provider about what side effects to expect and how to address them.