Are there any common complications resulting from arthroscopic surgery for a torn meniscus?

Yes. Any orthopedic surgery can result in complications like infection, blood clot or damage to nerves or blood vessels. These complications are very rare in arthroscopic surgery.
Yes. The risks for any anesthesia are allergic reactions to medicines and breathing problems. The risks for any surgery are bleeding, infection, bleeding into the knee joint, damage to the cartilage, meniscus, or ligaments in the knee, blood clot in the leg, injury to a blood vessel or nerve, and knee stiffness. Occasionally you may have a problem that simply cannot be fixed arthroscopically.