Any animal in the subkingdom "Parazoa" that includes sponges and
the trichoplax. These animals have no nerve cells or brain
whatsoever. If you are talking about animals that do have a nervous
system, it would probably be the Nematode "Caenorhabditis elegans",
or "C. elegans" for short. These creatures only have 300 neurons in
their entire body.
However, your question could also be interpreted as "What animal
makes the worst choices". Because, while C. elegans has 300
neurons, that's just enough for it to survive and thrive in it's
environment. If we are going by that logic, I'd say us, Humans.
While technically we are the most intelligent animal on Earth, we
as a whole have made terrible decisions that have both destroyed
our environment, and ourselves. We are one of the few animals that
kill our own species en-masse. Even so, this behavior is not unique
among Humans. Certain ants will kill other ants of the same species
in wars between colonies. I now notice that I'm going off on a bit
of a tangent, so to wrap it up, the answer really depends on what
you mean by "dumbest".