Towards the end of the movie, they showed an experiment where different mammals were placed on a digital scale, and monitored the creatures weight at the precise moment of death. They concluded that at the moment of death, the human body losses a few ounces of mass. The experiment was replicated with dog, a horse, and various different mammals, but found that it is only humans that registers a loss of mass. The experiment implies that at the moment of death, the soul vacates the human body, resulting in a loss of a few ounces. Here's a pict of the movie's DVD cover.

Of course there are animal ghosts. Animals have life, and they have death, so why shouldn't they have an afterlife as well? Limiting the concept to only humans seems an arbitrary distinction.
Indeed, it turns out to be a false distinction, if you accept the evidence of human ghosts. Witness accounts of animal ghosts are just as abundant as human ghosts. They also appear in photo anomalies and EVPs. They seem to remain earthbound for the same reasons as humans: Attachment to acquaintances and places from their life, don't know they're dead, want to protect someone, etc.
I can see ghosts so... I've even seen a dog!
I don't believe in ghosts - human, animal or otherwise - but I think that animals have spirits. Personally, there's only a few species that I think have spirits, not all of them. My spirit animal is the Bear, so I feel very strongly connected to them.