Beowulf encounters many "problems" in this epic poem. On the surface, these three "problems" can be identified as three different monsters whom Beowulf needs to fight.
The first monster Beowulf encounters is that of Grendel, who is attacking King Hrothgar's mead hall and killing all of his men. Beowulf arrives to defeat Grendel and save King Hrothgar's men from being butchered. However, once he defeats Grendel, Beowulf encounters another problem.
The second monster that Beowulf has to fight is Grendel's mother, for once Grendel returns home injured and dies, she seeks to avenge her son. Grendel's mother returns to King Hrothgar's mead hall and kills his best man in a type of "an eye for an eye" revenge killing. Beowulf must then confront Grendel's mother to ensure that all the evil of the land is gone forever.
The third and final monster Beowulf has to fight is a dragon who awakens and begins terrorizing Beowulf's land after a cup is stolen from its lair. It is during this fight that Beowulf perishes and relinquishes his land and power to the one soldier who stood by his side, Wiglaf.
However, something to note is that, although each of these monsters would be considered a "problem," the real underlying issue is the overall epic theme of good versus evil. Each monster Beowulf fights is a form of evil that must be overcome, and ultimately, Beowulf perishes at the end of the poem because he has an epic flaw that causes his demise. Once one succumbs to their innate desires (which can be viewed as a sin and therefore evil), they will die in mostly all epics.