1. Watch the bit where Lou gives the cats Professor Brody's formula for curing dog allergies. 'Mr. Tinkles', the cats' leader, says that he can reverse it.
2. Later the cats do indeed reverse the formula, so the serum they've created will make any human allergic to dogs, therefore ruining the dogs' hopes of world domination.
3. The cats give the serum to Professor Brody's son and when tested, it works- he's allergic to dogs. This should stay the same for the entire film, or at least until they get home and Professor Brody can cure him.
4. Later, outside the factory, after the place blows up, Lou is found lying, as if dead, on the concrete. Brody's son goes over to him and hugs him, crying, and talks about how Lou is his best friend. Lou responds, so he is alive (hooray!)
Wait a second.....
Lou is a dog! Brody's son is crying next to him, holding him, putting his face right next to his fur... why hasn't he experienced an allergic reaction? I wonder...
A copy of the film and a timeshare in Majorca.