When switching from survival mode to spectator mode, angry mobs will continue to chase you and attempt to attack. This continues even if you go into first person mode of another entity, although enemy attacks will only push them around rather than damaging them.

All of the normal AI is in effect. Specifically, getting far enough away from the angry mobs will cause them to stop being angry. Witches will throw harmful potions at you, and creepers will explode when they get close, and these effects can harm the entity you are spectating.