What kind of complications can you get from anesthesia?

Range of effects. If you mean general anesthesia (being completely asleep for surgery), the most common side effect is nausea. The anesthesiologist can give medications to help prevent nausea. Other possible side effects are sore throat and possibly sore muscles. Rare complications include malignant hyperthermia (a hereditary problem) and prolonged anesthesia effects. Most people tolerate anesthesia just fine.
Minimal. Post operative nausea and vomiting is the most common. There are really very few frequent complications of anesthesia. Tell the anesthesiologist every medication you take and all of your past medical history. Anesthesia has become very safe.
Nausea and vomiting. Modern anesthesia is very safe. I tell my patients that it is more dangerous to drive from the hospital to have the surgery than to get an anesthetic. The side effects that most patients experience revolve around nausea and vomiting in the immediate post-operative period.
Anesthesia. This is depends on whether its ga, local, nerve block or sedation. Issues such as reaction to drug, nerve damage, respiratory issues, damage to teeth, eye abrasions, death, being on a ventilator, feeling pain, etc.. Can all be complications. Without knowing the specifics this cannot be answered in this short space.