In a Parisienne musical number there are Can Can dancers and a woman wearing a short skirt made out of bananas (implied to be Josephine Baker.)

Dimitri and Anya share a long kiss at the end. Moments later, Bartok gets kissed by a female bat.

Sophie is a bit flirtatious.

In one scene Anastasia wears a strapless evening gown.

Anastasia slaps Dimitri across the face at least three different times, though only once was intentional.

Rasputin is seen drowning in the beginning of the movie after chasing the young Anastasia. After that, at the end of the movie, he appears to melt down to his skeleton, which then crumbles into dust and blows away with the wind.

None.

Dimitri and others have champagne at their table (but don't drink any) in a Parisian musical number. In a song Vladimir sings about a man loving vodka. People are seen smoking on the streets of Paris and one of the women hoping to pose as Anastasia is holding a cigarette holder with a smoldering cigarette in it.

During the scene where Rasputin sells his soul, his flesh is consumed and he's left nothing but a live skeleton, though his form is returned when he's given possession of the reliquary.

Rasputin has a reliquary that has a green, glowing substance inside as well as a snake running around the outside, and a human skull on the top. Small winged demons repeatedly come out of it.