While the Holy See has stressed in recent times that it is permissible to pray the Rosary during Eucharistic adoration, this has not been done with regard to Mass.
To my present knowledge, there is no law that expressly forbids one to say the Rosary during Mass, however this is implied by the laws that do exist. The Second Vatican Council and subsequent liturgical legislation have made it abundantly clear that the Church at present desires the faithful to have active, conscious participation in the Mass.
This does not mean that everybody has a job to do up in the sanctuary, but it does mean that everybody should be paying attention to what is happening in the Mass, giving attention to what the priest, lectors, etc., are saying, and so forth. Since the Rosary focuses attention on its own prayers and on the mysteries that it recounts, this would appear to diminish the faithful’s active, conscious participation in the Mass if said during Mass.
Thus saying the Rosary during Mass might fall into the “Please don’t eat the daisies” category of things that are not expressly forbidden but are clearly contrary to the intent of the legislator.
This does not mean that you can’t say the Rosary before or after Mass, but unless very unusual circumstances obtain, I could not recommend saying it during Mass. One’s attention during Mass should be on the Mass itself to the extent that the flux of human consciousness allows this, all things being equal.
