Unless you give it rapidly the minor complication rate is very small. (Transient drop in blood pressure).
From a recent Cochrane review:
Although being a relatively safe drug, it can cause severe systemic reactions with pronounced morbidity and mortality [1], and protamine sulfate is reported as one of the most common causes of life-threatening adverse reactions during cardiac surgery when used for rapid neutralization of heparin. Anaphylactic reactions to protamine sulfate have been known for many years, but the incidence reported varies from 0.06% to 10.6% [2] and range from minor haemodynamic instability to fatal cardiovascular collapse. The incidence of catastrophic reactions to protamine sulfate during cardiovascular surgery is reported to be 0.13% [3], and a recent study has con- ?rmed the relation between protamine sulfate reactions and mortality risk [4].
Reactions seem more common with diabetics that have received protamine-containing insulin, so maybe the current incidence is lower.