Quite a lot of "Simse.gameplay.core.null" listed as destroyed, and then what I'm used to (destroyed megaphones, pet descriptions, etc.). Is this anything worth worrying about?

I get those sometimes, trying to remember what is known to trigger them. I think returning from a vacation, Uni, or having recently switched actively being played worlds? Chain can confirm that for us again. But I don't think they are anything to worry about, especially if (hopefully) all seems as it should be in-game. By the time ErrorTrap gets its hands on "Destroyed Objects" like that, it's just leftover shards of data that have no place being in the game anyway.

Core.Null is a script class used for temporary items usually used in animations if I remember right.

That is correct, yes.