There is no actual sex or nudity, but the Nutcracker's genitalia are visible as part of the dancer's costume. It is never made clear whether or not this is intended as bawdy humor or to shock; in fact it is ignored so completely that the other characters in the story don't even seem to notice.
Drossel and Meier, a magician and his female assistant rather than the traditional Drosselmeier, are apparently romantically involved and kiss at the end of the first act.
After the Nutcracker is transformed into a Prince, Marie goes into a sort of "Sleeping Beauty" trance as he holds her in his arms; then, Prince Charming-like, he kisses her gently to awaken her.
At the end of their Act II Pas de Deux Adagio, it looks as if the couple might kiss again, but they are parted by a couple of competing dancers (who, it turns out, can't really dance).