(strayed)...all within recent history: (in 1854 and 1950 by popes who declared the Virgin Mary to be Immaculately Conceived and Assumed Bodily into heaven respectively) and (in 1870) when Vatican Council I declared the pope "endowed with infalibility, ex cathedra"... (not strayed) the Eastern Rite and Eastern Orthodoxy of the church--i.e. priests allowed to marry.
Rome considers Eastern Orthodoxy schismatic but not heretic because there are only relatively minor theological differences (such as whether the Son proceeds from the Father and the Spirit or the Spirit proceeds from the Father and the Son.)
If anything, the Eastern reverence of Mary is greater than in the West. It was a Greek council that first proclaimed her Theokokos (Mother of God.) Before the 11th century schism, Greek councils did not considered their rulings official without approval from the bishop of Rome.
Priestly celibacy is discipline and not a theological tenet. Ukrainian and Byzantine Roman Catholic priests are allowed to marry.
The Church cannot produce false doctrine because the Spirit guides it as Christ promised. When settling doctrinal disputes, the pope cannot fail since the Spirit would never allow error included into official Church teaching.
Error has ever been introduced. You may not believe this, but in 2000 years, no doctrine has been defined to correct a previous error. Can any other organization on earth makes a claim like this? The Church is definitely unique.
For 2000 years, the Church has never wavered from the teaching that she is the one true channel established by God for leading sinners to eternal life in heaven.