What current events are discussed while awaiting the ghost in Act 1 of Hamlet?

In Act I, we're brought up to speed on what is rumored to be going on in Denmark. A huge military buildup is underway, with bronze cannons being manufactured, weapons bought from abroad and so much shipbuilding occurring that the laborers are working seven days a week. Horatio explains that rumor has it that Fortinbras, the son of the King Fortinbras the late King Hamlet killed, is marching on Denmark, determined to avenge his father's death. This parallels Hamlet's quest to avenge his own father Hamlet's death on a larger scale. Thus, vengeance is everywhere. We also learn from Horatio, who references Roman times, that ghosts are a portent of danger. Later, in scene iv as the men again await the ghost, we hear from Hamlet that Claudius spends his nights drinking and dancing. Hamlet mentions that Denmark has a bad reputation as a place of drunkenness. 

This talk adds a sense of menace and foreboding to the play. With the country soon to be at war, it is easier to understand that Claudius and Gertrude would be all the more upset at Hamlet's seeming madness.

Most of what Marcellus, Bernardo, and Horatio are discussing is covered in the dialogue between Marcellus and Horatio in the dialogue quoted at length below. There is considerable military buildup in Denmark because an war is obviously expected. It could begin as a minor skirmish over some unimportant land but escalate into a full-scale war between Norway and Denmark. Horatio explains that young Fortinbras, heir apparent to the throne of Norway, has raised an army and seems to be preparing to reclaim certain lands which his father lost to Hamlet’s father, whose name was also Hamlet, in a duel. Horatio's following words explain the current conflict and sum up the discussion the men are having. This occurs mainly after Hamlet’s Ghost appears. “which is no other--As it doth well appear unto our state--But to recover of us, by strong hand And terms compulsatory, those foresaid lands So by his father lost: and this, I take it, Is the main motive of our preparations, The source of this our watch and the chief head Of this post-haste and romage in the land.”

The following exchange is the crux of the current events being discussed.

MARCELLUS

Good now, sit down, and tell me, he that knows,
Why this same strict and most observant watch
So nightly toils the subject of the land,
And why such daily cast of brazen cannon,
And foreign mart for implements of war;
Why such impress of shipwrights, whose sore task
Does not divide the Sunday from the week;
What might be toward, that this sweaty haste
Doth make the night joint-labourer with the day:
Who is't that can inform me?

HORATIO

That can I;
At least, the whisper goes so. Our last king,
Whose image even but now appear'd to us,
Was, as you know, by Fortinbras of Norway,
Thereto prick'd on by a most emulate pride,
Dared to the combat; in which our valiant Hamlet--
For so this side of our known world esteem'd him--
Did slay this Fortinbras; who by a seal'd compact,
Well ratified by law and heraldry,
Did forfeit, with his life, all those his lands
Which he stood seized of, to the conqueror:
Against the which, a moiety competent
Was gaged by our king; which had return'd
To the inheritance of Fortinbras,
Had he been vanquisher; as, by the same covenant,
And carriage of the article design'd,
His fell to Hamlet. Now, sir, young Fortinbras,
Of unimproved mettle hot and full,
Hath in the skirts of Norway here and there
Shark'd up a list of lawless resolutes,
For food and diet, to some enterprise
That hath a stomach in't; which is no other--
As it doth well appear unto our state--
But to recover of us, by strong hand
And terms compulsatory, those foresaid lands
So by his father lost: and this, I take it,
Is the main motive of our preparations,
The source of this our watch and the chief head
Of this post-haste and romage in the land.

Now, Shakespeare wanted to introduce the Ghost before young Hamlet encountered him in the final scenes of Act 1. But Shakespeare had several problems. One was to introduce the Ghost as a ghost. He didn’t want to have old Hamlet wearing a spooky-looking white shroud. So he had all three observers testify to one another that the bearded actor wearing armor was indeed a ghost and looked exactly like the former king. Every time this character appears in his armor, the audience will understand that he is a ghost and he is Hamlet’s dead father. That was Shakespeare's reason for introducing the Ghost to Marcellus, Bernardo, and especially Horatio before Hamlet ever encounters his dead father. Shakespeare did not want to have a character in armor suddenly appear to Hamlet and say something like, "I am your father's ghost." The audience wouldn't be prepared for it. There would be a lot of awkward dialogue regarding the Ghost's identity before the Ghost could get down to the real purpose for his visitation.

Bringing in the discussion of Fortinbras and the threat of war at this point, along with the identification of the Ghost, is apparently a red herring, a tempest in a teapot. Shakespeare did not want his audience to suspect the true reason for the Ghost’s appearance, which was to tell his son that he had been murdered by Claudius, his brother and Hamlet’s uncle. Shakespeare dresses the Ghost in armor both so that he will look rather strange and so that the audience will think he is really there at Elsinore because he is concerned about the threat of war. After all, it was old Hamlet, the former king, who created the present conflict by killing old Fortinbras and winning certain unimportant lands which are now being disputed by young Fortinbras. But this threat quickly evaporates. Everything is settled through offstage negotiations by Act 2. The real purpose of the discussion of the war threat and military preparations was to distract the audience, so that the Ghost’s revelation to his son in Act 1, Scene 5 will come as a complete surprise to young Hamlet as well as to Shakespeare’s entire audience. The audience must believe the Ghost is there because he is concerned about the war threat and not to tell his son that he had been murdered by the usurper King Claudius. That is why the Ghost is wearing armor, but it will also identify him as the Ghost.

Once Shakespeare created young Fortinbras and his army, he continued to use the aggressive young warrior as a sort of subplot, but Fortinbras does not appear in person until the very end of the play. He is really a minor character and never a serious threat. Hamlet even nominates Fortinbras to become Denmark's ruler with his last dying words.