The two issues have generated a flurry of headlines in recent days, sending commentators scrambling to explain their significance for the Argentine pontiff and his battle to reform both the way the Church is governed and its message.
Conspiracy specialists have also been working overtime on the emergence last week of a leaked - but apparently falsified - document, purporting to point to a Vatican cover-up. This relates to a 33-year-old mystery over the disappearance of the Emanuela Orlandi, the 15-year-old daughter of a Vatican employee.
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Interpretations of the recent spate of intrigue vary but the one thing they all agree on is that Francis is under fire.
In recent days the 80-year-old has found himself accused of throwing in the towel on cleaning up how the Church handles its vast wealth and of propagating heresies on divorce and other issues.
Three months after he suddenly quit as the Vatican's auditor general, Libero Milone broke his silence at the weekend to claim Vatican officials had conspired to block his access to Francis because "they didn't want me telling him about some of the things I'd seen."
In the face of the resistance, the pope had become disillusioned with a task he had previously regarded as a priority, Milone suggested.
Almost simultaneously the heresy charge was tabled by a group of clerics and lay theologians, some of whom are linked to the Society of St. Pius X, an ultra-traditional, breakaway group founded by the late French Archbishop Marcel Lefebvre.
In a 25-page open letter dubbed "A filial correction concerning the propagation of heresies," the group indict Francis on seven specific counts of heresy, born of what they term a mistaken modernism and sympathy for the teachings of Martin Luther, the founder of the Protestant reformation in Europe.
The most notable heresy charge relates to the pope opening up the possibility of some divorced believers receiving communion, which critics see as undermining the principle of the indissolubility of marriage.
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Photo: Alberto Pizzoli/AFP
The dissidents have talked up their document as the first challenge of its kind to a pope since 1333. But most observers have been quick to dismiss them as an insignificant fringe.
"It is a small, very unrepresentative group," Vatican expert Iacopo Scaramuzzi told AFP, noting that none of the Church's 5,000 official bishops had signed up to the document.
It does however echo more influential criticism of Francis's position on the divorce-communion issue outlined in his 2016 publication on the family, "Amoris Laetitia" ("The Joy of Love").
Later that year, a group of four cardinals led by American Raymond Burke put their reservations about "Amoris " on record in a series of questions, known as "dubia".
Francis has yet to respond but the cardinals, two of whom have since died, have not acted on a threat to elevate their complaint to a formal "fraternal correction".
It is this background that has led some analysts to conclude that the latest initiative is about prompting Burke and co. into a high-stakes open mutiny against the skipper of the Catholic ship.
American Vatican watcher John L. Allen Jr says that amid all the talk of traditionalist scheming, more important questions will be overlooked.
"There's a risk that the very serious suggestions being made by Milone about the state of Francis's much-ballyhooed financial reform will be drowned out by the noise generated by everything else," Allen wrote on the Crux.com website.
Milone did not offer details of the alleged irregularities he says he became aware of, citing a non-disclosure agreement. His comments sparked a furious reaction from the Vatican, which took the unusual step of publicly stating that he had been pushed out because he had been spying on senior officials.
The Vatican has won praise in recent years from a European financial watchdog for cleaning up the scandal-tainted Vatican Bank, albeit qualified by criticism over a lack of follow-through prosecutions.
But concerns the reform process has not been as far-reaching in other parts of the Vatican bureaucracy linger and have been highlighted by the ongoing trial of two former officials accused of embezzling funds from a Vatican-run hospital.
The cash was allegedly used for the costly makeover of a luxury flat occupied by an Italian cardinal who has not been required to give evidence in the trial.
By Kelly Velasquez and Angus MacKinnon