My dear friend, you have opened a can of worms here and no doubt will get many interesting replies. Since I’m up late, I’ll start with a simple one. This is a particular Rite that was one of the Mass options used before Vatican II. Some people just refer to it as “the way the Mass was before Vatican II” but there are some distinctions. But the key thing to know is it’s in Latin, follows the old practices of priest facing away from the congregation, is very formal, takes several hours. Some of it is just the form people love, candles, incense, chanting, etc. Others will fill in here with technical details, I just want to paint the big picture.
Now, the Tridentine Mass cannot be performed without permission from the bishop. Several decades ago, a little trend started here and there, mostly among old folks nostalgic for pre-V2 days, requesting this Mass. Then young people yearning for more traditionalism and tired of twanging electric guitars started to experience the beauty of the Tridentine Mass for the first time.
But now it has become controversial because of the SPPX’ers. (They name themselves after St. Pope Pius X.) These people have split off from the Catholic Church, they believe the Pope was not validly elected and is therefore not the Holy Father (the See is vacant), they perform this Mass and believe everything from Vatican II is invalid. They are in schism. The Pope has reached out to these folks to try to get them to rejoin the church, but basically they are heretics (even though possibly with good intentions).
Sadly, because of this, permission for the Tridentine Mass is now being withheld in certain diocese, or withdrawn. Although regular practicing Catholics may attend one if it’s offered by a Church in good standing, do be careful of being lured into a schismatic organization.
Mel Gibson’s father is one of these radical SPPX’ers who reject everything prior to Vatican II. Mel Gibson himself, sadly, is not really completely well-grounded in the Catholic faith, having being influenced by his dad, but because of his movie, he had tried to walk a fine line and seem like a “regular” Catholic. He is very devout and my hope is that he has gotten good advice from Priests and laypeople and will embrace TRUE Catholocism, and abandon some of his wacky ideas for starting his own church.
The Tridentine Mass is not right or wrong unto itself. If it’s performed with the permission of the bishop by a priest in good standing, in a Catholic parish or mission, no problem. But the SSPX’ers have sort of taken it over, and this is where people are getting confused. Well, I better let others contribute, I know on this site there must be some very good experts on this matter