In brief (I’m tired, and have posted on this a lot, but I’m not sure where: if ECF, you can’t get at it).
Formosus had been laicized, and Pope John VIII convenved a synod and extraced an oath by Formosus that he never return to
Rome and exercise priestly function. Pope Marinus I then restored him to his see, and then Formosus was elected Pope. He ordained the future Stephan VI, who, once he was elected, nullfied Formosus’ papacy and all his ordinations, including evidently his own (he dug up Formosus’ corpse and tried him). Then Pope Theodore reverse this, while his deposed predecessor Pope Romanus still lived (and thus should be the legitimate pope). Then Pope Christopher came (now for a century considered an anti-pope), who was succeeded by Pope Sergius III (excommunicated by Pope), who dug up Formosus again, reimposed Stephen’s decisions and demanded that all the hierarchs ordained under Formosus had to be reordained, (he murdered popes Leo V and Christopher), a decision then reversed by Pope Anastasius III. And I’ve actually left out quite a few details.
Now (except for the modern view of Christopher) we are dealing with popes who are all seen as being legimate who are annullying each other’s papacies, excommunicating, defrocking, etc. calling into question the episcopal character that a pope must have according to canon, and the validity of the election (excommunicated and the invalidated episcopate don’t validl elect). Which is a problem if your source of unity comes from the pope.
With an antipope, the issue is even deeper, as who is an antipope is mostly determined by hindsight (Christopher wasn’t struck from the official list until over a thousand years after his death).
Now I have always said the problem is that the pope, according to Latin theology, is ontonlogically different from other bishops (infallibility for one) and questioned why that is not reflected in an ordination to the papacy. I’ve been told the election is the elevation, and his powers come from that (problematic). Now if you have an irregular election, what does that do to the pope’s status? The transmission of a unique charism (which the latin church claims for the pope) makes a unique problem: if any other bishop, three other bishops (or one in an emergency) could pass the charism on. But the pope claims a charism above the faculty of the bishops.