I've never been a fan of the ghost. He wants Hamlet to avenge his death seemingly for his (the ghost's) own satisfaction, not to re-establish social justice or for the sake of justice itself. The farthest he goes beyond himself seems to be:
Let not the royal bed of Denmark be
A couch for luxury and damnèd incest.
At least he's gotten out to some matter of state, but wouldn't you know it's one that not-so-coincidentally is also a matter of intense personal resentment.
Hamlet does wonder whether the ghost is a seductive demon, since demons will assume pleasing forms in order to tempt humans to foul deeds. But as far as I can tell Hamlet never questions his father's love. He never asks, If my father loved me, why would he order me to commit the same kind of deed for which he's now suffering horrible tortures in Purgatory? In fact, Hamlet in his reminiscences of his father never says anything about what a great dad he was or how affectionate he was; he talks about what a paragon of kingliness he was, what a fine figure he cut. Yorick is the guy who made little Hamlet laugh and bounced him on his knee. Maybe the ghost figures Hamlet, unlike himself the ghost, will get a chance to repent and receive absolution before death, but you certainly never see the ghost say "Make sure for heaven's sake to have a priest handy when you go to stab Claudius." NOOO, it's just "Remember me."
It's true, Hamlet characteristically generalizes his situation whenever he contemplates it and sets all his considerations in a philosophical, not personal, context, but it seems to me the question of his father's character -- his psychology, his love -- could also be considered that way.
Anyhow, I can't find that Hamlet ever asks a question that to me seems quite obvious. Or does he? Am I missing it somewhere?
I have another few complaints/questions about the ghost's character coming up.