Not within the usual modern definitions. A man marries his brother's widow, which has been considered incestuous in some times and places, and is described as such by one character within the story.
Gertrude gets with Claudius after the death of Old Hamlet. It's not technically cheating, but kind of a d**k move (edit: though admittedly she's likely doing it for the good of the kingdom).
Claudius overindulges in drinking in Act 1 Scene 4 and has a single drink in Act 5 Scene 2 (the final scene; it would be detrimental to skip this). Still, there's nothing to suggest it's a chronic problem.
There are mentions of Hell in dialogue, but it is not depicted on screen. There is an apparition that's suspected of being of diabolical origin, though it's usually interpreted as being, in Hamlet's words, "an honest ghost"; apart from that, there are no demons.
The Gravediggers in Act 5 Scene 1 are called clowns, and Yorick (who appears solely as a skull in this scene) was a jester when he was alive. They aren't clowns in the modern sense, though. They don't look like modern clowns in the 1996 version, as in most versions of Hamlet.
I'm assuming someone said "yes" because a character could be interpreted as a minor, but her age is never given in this movie or original text. The actress playing her is 19.
Hamlet's father died before the movie starts, and he is still grieving throughout. His mother and stepfather die in the course of the movie, as does the father of Ophelia and Laertes.
Hamlet's deceased father appears as a ghost four times (Act 1, Scene 1; Act 1, Scenes 4 and 5; and Act 3, Scene 4). The nature of his ghost as a devilish figure versus as a legitimate apparition is a matter of debate, however. This page pertains to the 1996 film of Hamlet but it is worth noting a few productions, like the Meno Fortas one, have the Ghost's role more prominent.
Ophelia drowns; this is reported by Gertrude in Act 4, Scene 7. I can't think of any production that shows the drowning onstage or onscreen, though, and whether Ophelia's drowning is an accident or a suicide isn't 100% explicit.