While this anime is very well-done, it does have a lot of problematic content
Nudity/Sexual Content
While there is no explicit sexual content in the anime, there are inappropriate relationships, and it's often heavily implied that various characters are having sex with each other, and some characters are shown in bed together. There are several incestuous relationships, although only one of these is sexual. To be fair, it's not portrayed in a positive manner, and can easily be considered abusive.
Utena is considered a shojou-ai (girl's love) anime, and so it's implied that the two main female characters are in love with each other. This is open to interpretation, but there are still strong shojou-ai implications between them. There is another female character who is in love with a girl, and it is not just implied, but her feelings are unrequited.
The nudity is undetailed.
Violence: There is very rarely any violence in this apart from the sword duels, in which the goal is not actually to kill the opponent. However, there is one reoccurring scene toward the end of the series where a character is pierced with many swords at once and remains alive. We only see their silhouette, though.
To sum it up, while this is often considered an excellent anime, there are a lot of sexual implications, and it should be viewed with caution. It's not recommended for anyone under sixteen.