Minecraft wiki entry for Spectator, associated text: If the player wears a pumpkin on their head and enters Spectator mode, their vision will still be filtered, even when spectating a mob.
If an entity falls out of the world, any spectators will die with it as they are still separate entities, and will take void damage.
All mobs' perspectives can be viewed with the exception of the ender dragon.
Shaders will persist if the player dies while spectating.
In the Chinese version, it is possible to access this mode in multiplayer by changing the "trust player" option, which makes new players to spectators.
In Bedrock Edition, when a player enters Spectator mode using an NBT Editor, mobs will still observe them, but will be unable to interact.
If a player has an effect applied that changes their fov, players spectating them will also be affected, nausea being the exeption. The FOV changes are not visible when spectating non-players.
If a player uses a spyglass, the effect will also apply to the spectator, but without the overlay.