Usually very minimal. The standard risks of any procedure are possible, such as: infection, nerve or vessel damage, and clot. These potential complications are rare and occur generally less than 1% of the time. Other procedure/disease specific complications may include persistent pain, stiffness, weakness, and a need for further surgery. Discuss your surgery thoroughly with your surgeon.
Pain and stiffness. The most common complications of shoulder scopes would be pain and stiffness, or a frozen shoulder. Good post-op therapy should help prevent this. Other less likely complications include nerve injury about the shoulder, infections, and anesthesia reactions. Relative complications include failure of surgical repair or recurrent tears.
More Information. Along with the other excellent answers, here is more information on this topic for you: http://www.Theshouldercenter.Com/shoulderpain/2010/shoulder-surgery/shoulder-surgery-complications-an-ounce-of-prevention/.
Several. Overall rate recently reported 4.6-10.6%; comps include nerve traction injuries, spinal or cerebral ischemia (rare but serious), complications from nerve blocks, chondrolysis or other cartilage injury, nerve injury, infection, blood clots (dvts); other issues are repair failures/re-tears, postop stiffness (frozen shoulder)... Overall they are safe, most comps are transient; talk to your surgeon.
Pain and stiffness. The most common complications are pain and a failure to return to your prior full range of motion. General surgical complications, such as infection, bleeding (hematoma formation), or damage to surrounding nerves or blood vessels are all possible but occur less commonly with arthroscopic surgery. Other possible complications depend on what procedure you are having done with the arthroscopy.