Question

at the start of act 1, what do the watchmen and horatio speculate the appearance of the ghost means?
denmark is about to win an important battle.
someone is playing a practical joke on them.
denmark is inhabited by thousands of similar spirits.
something is very wrong in denmark.

Explanation:

In Hamlet, the appearance of the Ghost at the start of Act 1 is a portent. The watchmen and Horatio, being aware of the political and social context (the recent death of the king - Hamlet's father, and the hasty marriage of Gertrude to Claudius), view the Ghost's appearance as a sign that something is amiss in Denmark. It's not about a practical joke (as the Ghost's demeanor is serious and its appearance is recurrent in a solemn setting). There's no indication in the text that Denmark is full of similar spirits or that a battle victory is impending. The overall mood and the events (like Fortinbras' threat, the abnormal succession - Claudius taking the throne instead of Hamlet) support the idea that the Ghost's appearance signals a deeper problem in Denmark.

Answer:

Something is very wrong in Denmark.