I've just installed Morroblvion and it is working, so far at least. But every time I start a game or load a save it says I am missing one or more core BSA files. I use Mod Manager and every BSA that was in the morroblivion_v64_complete.7zip file is showing and checked in the Archives area managed by MO. These are the meshes, textures and sound bsas. I also have the conversations bsa but that's not a core file. Am I missing something?
Did I say Mod Manager before?
Did I say Mod Manager before? Sorry about that. I use Mod Organizer, so the BSAs aren't physically in the Data folder but do get loaded in along with other mods that also aren't really in the data folder either. I am seeing very different models and textures from what I used to see when playing Morrowind and spell casting and blocking are the same as Oblivion's. As far as I can see, everything is working.
I use Mod Organizer, so the
I use Mod Organizer, so the BSAs aren't physically in the Data folder
Well, that's the source of the error.
Personally, I do not approve of the way Mod Organizer does things, but if you really want to use it and your game is working, you can just disable error detection in Morroblivion.ini file.

What mod manager are you
What mod manager are you using? Check if Morroblivion BSAs are in Oblivion\Data folder with Windows Explorer.
Also, is you game working correctly? As in, do you actually see Morroblivion-specific models and textures?