How much brain power does it take to realize that a creature that doesn't look, smell or act in any way like a cat is not a cat? How would it be different from realizing that mice and dogs are not cats?

Enough brain power to come up with the concept of "being a cat", then leading to discriminating the environment between "is a cat" and "isn't a cat". Whether cats do is anyone's guess.

That said, cats probably have enough brainpower to come up with the concept of "I'm me". Just watch a cat, or a dog for that matter, looking at itself in a mirror if you need convincing.

"Take care of me" and "feed me" are pretty established too.

You are making assumption that cat's brain works the same as human's brain. Maybe that's good assumption but question is how good?

Have you seen this TED talk http://www.ted.com/talks/jill_bolte_taylor_s_powerful_stroke... ? "being a cat" is related to self-awareness. Does cat has the same self-awareness as human beings?

You are making brave assumptions here, aren't you? Dogs = unfriendly cats that smell bad and look ugly, mice - edible cats that smell tasty and are small.

It might look like this: http://www.youtube.com/watch?v=HPeattKV74A

Again that's just speculation. I would love to see scientific data here.

You would see far more feline on feline predation if this were the case though, wouldn't you?

It depends on the difference between a cat-cat and cat-mouse.

You've renamed everything as cat. But the problem remains the same.

I guess that changes problem slightly. Different criterions are chosen when taking actions. E.g.: Can I eat it? No - too big. No - smells bad. Two inputs - one output. Can I mate with it? No - smells bad. No - too weak.

While being human you might have much more sophisticated criterions and first criterion might be "is it human?". Most probably how it smells and how big it is will not be enough.

They realize that a dog or a mouse is not a cat, don't they.

I don't know. I guess they do but most probably not in the way we do it.