The monster is a capibarra, a wild pig/rat from South America, it is considered a delicacy in Brazil. Taste like Chicken! I've had it and its not bad. To prepare it you can drop it boiling water to remove the skin, then roast it.
A foreign pig, eh? That would sure explain this picture of Monty acting like a terrorist (left), courtesy the brand new Montauk Monster mash-up site.
But there's one problem with focusing on the lack of upper teeth, as in the pig theory: The skull as show in the original, more decomposed picture of the monster looks like it has sockets for teeth on the top.
These sockets would be critical not only to the dog theory, but also the raccoon theory, as illustrated in this image from a chat board discussion:
And of course, pigs have some upper teeth, too, so the sockets don't rule out Monty being a pig.
But it's worth noting that monsters and demon hellspawn are known for bad dental hygiene, so there's always that!