Is it permissible to say, "Allah willed [or 'intended'] Dr. Muhammad Morsi," given the difference between irada (will/intent) and mashee'a (wish/decree)?

Both "Mashi'ah" (Will/Desire) and "Irada" (Intention/Purpose) can be used interchangeably, but there is a distinction between cosmic will (Irada Kawniyyah) and legislative will (Irada Shar'iyyah). The cosmic will is bound to occur, whether it pertains to what Allah loves or dislikes. As for the legislative will, it only pertains to what Allah loves, and it may or may not occur. When one says "what Allah willed," if the cosmic will is intended, then it is true. If the legislative will is intended, then that depends on whether the doctor is more competent and closer to obeying Allah and establishing His religion. It is safer to avoid such phrases.