I have observed a local priest giving the host to a couple I am certain he knew to be nonCatholics. When I asked my parish priest about this, he shook his head, said that it was certainly wrong but told me not to worry unduly. Last Sunday I saw him do the same for an attendee at our mission church whom he knows to be a professed Lutheran. I am believe these acts are violations of Canon Law (844). Should I ask the diocese for clarification?
These links should be helpful for understanding why non-Catholics should not take Communion at Mass. If you have any further questions or concerns that are not answered by these links, please contact Catholic Answers directly.
*]Who Can Receive Communion?
*]Ecclesia de Eucharistia **(Note especially sections 43-46)