What are common anesthesia complications I should be aware of before surgery?

Nausea. Ponv - postoperative nausea and vomiting are the most common and usually easily treatable. Allergic reactions, stroke, negative pressure pulmonary edema, sore throat, blindness, heart attack, malignant hyperthermia, death are very remote possibilities and should not prevent you from having surgery. Discuss your concerns with anesthesiologist. Modern anesthesia is very safe.
Mild and transient. If you are having general anesthesia and will be paralyzed then common complications can be: sore throat, muscle aches, nausea, swollen vein by IV site. Less common: broken tooth, scratched cornea, neuropathy , urinary retention and pulmonary problems. Of course there are rarer and more serious complications.
Sedation, and nausea. The common effects of anesthesia are initial sedation and the possibly nausea and vomiting. These side effects are easily managed by an alert pacu staff. Please contact you anesthesiologist with questions before your procedure.
Nausea and vomiting. This is by far and away the most common complication. The other side effect, not really a complication, is that you can expect a sore throat. All other potential issues and complications are so rare that they are not worth mentioning or having you worry about.