Many Catholics have said we can't be certain of the Truth of what happened in the Vatican in the late 60s and 70s, without a special revelation from God and Our Lady. Well, it so happens that there is such a revelation, and not just one made recently in this year 2019. A good place to start would be Our Lady's revelations in Akita, Japan. But even beside those revelations in Japan made to Sr. Agnes Sasagawa, where Our Lady condemned infiltration, destruction of Altars etc, in the 60s and 70s, there is another, namely Our Lady of Bayside, made to Mrs. Veronica Lueken, a Catholic Mother of 5 children, in Bayside, New York. See for e.g. ""My Son is not pleased with the manner in which His Body and Blood is being given to all of the humans upon earth. "Communion in the hand has not been, and will not be accepted by Heaven. This is a sacrilege in the eyes of the Eternal Father, and must not be continued, for you only add to your punishment when you continue on in the ways that have been found to be unpleasing to the Eternal Father.
Conservative Catholics generally disdain Bayside, because it clearly says the TLM is vastly superior to the NOM, obtains far greater graces, is much preferred by Heaven, was never abrogated and every Priest can freely offer it, that there had been a very severe infiltration into the Vatican (although not precisely in the way sedes think - for e.g. with Cardinal Casaroli, Villot and Benelli altering Papal letters during Pope Paul VI's time, and then conspiring, and actually killing Pope John Paul I) etc.
Our Lady had said similar things in Akita, but She did so more implicitly and reservedly, because the Hierarchy was hostile even to that.
There are a number of testimonies about supernatural phenomenon, just as at Fatima or Lourdes of old: https://www.tldm.org/testimonies/testimonies.htm
Our Lady also gave a clue about the Third Secret of Fatima, ""My children, long ago I warned you from Fatima, I warned you through many voice-boxes throughout your world that the time will come when you will embark upon a stormy sea, and it shall be bishop against bishop and cardinal against cardinal [this warning is remniscent of Akita also - often Our Lady "cross-verifies" Her own apparitions across the globe], and satan shall set himself in your midst."
- Our Lady of the Roses, November 20, 1976
Now, finally, a good place to begin investigative research about whether all of this holds up would be the public death of H.H. Pope John Paul I. It is universally known he died 33 days after becoming Pope. The messages at Bayside said he was actually murdered: "“We will go back, My child, in history, a short history, and remember well what had happened in Rome to John, Pope John, whose reign lasted 33 days. O My child, it is history now, but it is placed in the book that lists the disasters in mankind. He received the horror and martyrdom by drinking from a glass. It was a champagne glass given to him by a now deceased member of the clergy and the Secretariat of the State [Cardinal Villot].”
- Our Lady of the Roses, May 21, 1983 https://www.tldm.org/news3/johnpauli.htm
Does the explanation hold up? Yes, there's good evidence for it. Fr. Georges Nantes, who didn't believe in Bayside as far as I know, independently arrived at the same conclusion, ""in an amazing manner, Cardinal Villot’s activity during the twelve hours following the crime to make it look like a natural death. This exploit would constitute the most successful of « perfect crimes » ... Villot : « What occurred was a tragic accident. The Pope had unwittingly taken an overdose of his medicine. If an autopsy was performed it would obviously show this fatal overdose. No one would believe that His Holiness had taken it accidentally. Some would allege suicide, others murder. It was agreed that there would be no autopsy. »The explanation is crazy : how could one know what the poor dead man had done, alone and without realising it ? It is improbable : the Pope’s medicine, Effortil, cannot be the cause of sudden death in one suffering from low blood pressure, even if the dose were doubled or trebled. It is defamatory : it insinuates the idea of a poor pope overwhelmed and out of his depth committing suicide. It is untenable : if it were really believed, on the contrary every precaution, delay and necessary assurance would have been taken to stop the assassination thesis gaining ground and to exculpate oneself from these accusations before a tribunal.From the way Cardinal Villot formulated and imposed such an alibi, he reveals himself as a Master, a Grand Master of the masonic secret. Furthermore, he performed his role, his check-up, quite imperturbably, with a perfect mastery of himself, the Church and events." http://crc-internet.org/our-doctrine/catholic-counter-reformation/murder-john-paul-i/1-murder-vatican/