When Russian soldiers attack a group a protesters, we see many of them hit with swords. No one dies, but some are knocked out.
When Tevye looses his temper he often shouts and yells, which could be frighting for younger audiences, and even some adults, as it sometimes comes as a surprise.
There is a somewhat emotional parting between Tevye and Hodel, as she leaves to be with her fiancé imprisoned in Siberia.
There is a dream sequence that takes place in a graveyard. All of the departed pop out of graves, but are not evil or menacing. The whole sequence is in song. It is so comically over-the-top, that it will not be scary for most.
This film deals with subject of antisemitism in Czarist Russia. The pogram scene is shocking, as soldiers attack the Jewish half of a village.