Mike is right with the foreshadowing.
Note how nobody likes Candy's dog because it smells, it's old, it's useless and it's brainless. They urge the dog to be shot dead; this foreshadow's the death of Lennie in the end - as he too is a threat to the group, he's useless and brainless. At the end of the day, Lennie is essentially a murderer but due to the time the book is set, they don't realise his mental abilities and the amount (or lack of) control he has over his actions.
And therefore, is it fate that Lennie is being compared to a dog? Lennie has the same mental ability as one. He's compared to many animals, including a bear "dragging it's paws" and "dabbling it's paw in the water" - Lennie is essentially an animal. He's mis-understood, unable to realise his problem; and that is the whole point of the book.
I think I wrote all that terribly so I might reply here again tomorrow I quite enjoyed of Mice and Men though - hey, it got me an A!