Is there any special meaning to the way Paul so often wishes his readers "grace and peace"? 

There is. In the east, people wished one another "peace," just as the Jews said "Shalom" and the Arabs "Salaam." In the west, a standard opening for an epistle was "Greetings" (Greek chairein, as in Acts 15:23). Paul, the apostle who preached the gospel to Jew and Gentile alike, combines the terms, as in Philippians 1:2. "Grace," charis, is similar to the word chairein. Thus in Christ we acknowledge the "grace and peace" the Lord provides. This very greeting is an emblem of unity.