The Mormons have the division problem themselves-- There is the Church of Jesus Christ of Latter-Day Saints in Utah, but also the Reorganized Church, the Jacobites(if i have the name right), etc. etc. Futher, they get their start in about 1880 when an angel came down and talked with Joseph smith and led him to find another book. Tell me, did God wait till about A.D. 1880 to get his Church back together?

As for Catholic unity, the term "catholic" is used as much as the term "Christian" by individuals and churches. There are numerous Catholic groups not in submission to the Pope. Some are more like Protestants, others more like Catholics in faith and practice. Some are highly liberal and ecumenical and others very conservative and separated.