When Jake morphs his dog Homer, he sniffs Tobias' shoe. He describes a dog nearby, that he shouldn't know by smell, since he doesn't have Homer's memory. He also says 'He was neutered, just like me', when the Homer morph would be intact. It runs on DNA, remember?
Jake the human knows the dog, and Jake the dog could smell what he looked like, so Jake would know the dog by smell. And when he said neutered just like me, he meant just like Homer, because Jake is Homer and he didn't know that he wasn't neutered, they don't figure that out until later.
Mindy Doll, the whole point of this slip-up is that morphs go by DNA. When you morph, your body changes according to the morph subject's DNA. When a dog is neutered, its DNA does NOT change. Thusly, the Homer that Jake morphs into should not be neutered.