The movie implies that the earthquake that devastated Cephallonia after World War II occurred in 1947. It was actually in 1953. At the end of the credits, the movie is dedicated to the memory of those who died in the post-war earthquake of 1953. The DVD commentary also mentions the correct date.
The goof items below may give away important plot points.
A radio broadcast announces that the Allies have taken Rome. This leads to Italy dropping out of the war and fighting between the Italians and Germans. Italy surrendered in September 1943, after the Allies captured Sicily. Rome fell in June 1944, long after all of Captain Corelli's men were dead.
Captain Corelli says "Mussolini has surrendered to America and Britain, not Germany". Benito Mussolini didn't surrender to anybody; he was arrested by his fellow Fascist Party Council members, supported by some Italian Generals and King Victor Emmanuel III of Italy. After he was rescued by Adolf Hitler's SS commandos, he continued to fight the allies.