This is a super odd one. I've seen a report where a user is playing in single player with ReplayMod and all is just fine. If they open the game to LAN and add a second account in spectator mode, the spectator account sees a dragon rendered. It appears to have no AI (it's stationary but it's wings flap). It doesn't appear to actually be in the world as no blocks are damaged and the original player in survival can't see it.

The dragon also isn't present in the replay editor, it's only there for the spectating player in-game. There have been instances of multiple dragons being present, all with the same behaviour as above.

If the user does the same as above in the same world but without replaymod installed the dragon doesn't appear to it seems replaymod is adding this entity for the spectating player.

That's very odd indeed. No clue how that could even happen and have had no luck trying to reproduce it by walking around a normal world or flying around a flat world for five minutes each.

Are the dragons consistent across time and/or re-connects or do they appear in different places each time the chunk is loaded?
Is there anything notable in the real world at the same position as the fake dragons?

A forced crash report (press and hold F3+C until it crashes, about 10 sec iirc) of both, the spectating client and the hosting client, might be helpful (cause they contain info on all the entities in the world). That would also answer any question I might have about which mods were in use on which client.