So in one of my earlier post, I mentioned that in Not What He Seems, Stan was operating the Portal, and he wiped his sweat from his forehead. But when he did that, he smeared his forehead with nuclear waste as well, and his forehead absorbed it. So what did it mean? Did it have an impact on the show? To which I say now because I suddenly realise, yes, perhaps.
I don't know if it's just me, but I noticed that Stan's Mind in Weirdmageddon is totally different from that of Dreamscaperers. In Dreamscaperers, Bill, Dipper, Mabel and Soos enter Stan's mind, and it was a Mystery Shack full of memories everywhere. But in Weirdmageddon, when Bill enters, there's nothing there, only a door to the TV room of the Mystery Shack. This would explain why Stan said "Welcome to my mind. Surprise you didn't recognise it." Because he knew Bill entered his mind before, and thought that Bill should have had recognised it earlier, but the exterior was gone. So that would mean the exterior of his memories were wiped out with the nuclear waste absorbed, but Stan didn't realise it, probably because in his mind, his consciousness resides in the TV room.
The reason I said Stan knew Bill entered his mind before is because although Stan was asleep, Bill entering his mind could have become part of his dream. Whenever we have a memory of something, it is bound to appear in our dreams, one way or another. This time though, in Dreamscaperers, Bill entered himself. So maybe Stan did know that Bill entered his mind, but earlier thought it was a dream. So when he saw Bill during Weirdmageddon, he knew that it wasn't a dream at that time, and so told Ford that Bill could enter his mind again.
In conclusion, my theory is that the nuclear waste helped destroy the exterior of Stan's mind, so that Bill wouldn't recognise it at the start. If there wasn't any nuclear waste, the Mystery Shack mind would still be there and Bill would realise it and come out.