It's a fish.

Specifically, what I found are the pharyngeal teeth of a grass carp, a
fish native to Asia and probably stocked in the pond to control
vegetation overgrowth. Ashe's friend's identification of "carp" had led
me to find some images on google and figure it for a grass carp, and
then I just now got a note from Missouri Wildlife Division that says,
yup, that's what it is. As likely as not the rest of the bones belong to
the same fish, even if they were found several feet away.

If we hadn't been so certain it was a mammal, we might have found it on
google ourselves. Whyever didn't it occur to us to look at fish
skeletons since 1) we knew we had most of a fish skeleton anyway, and 2)
it was found in a pond! I knew perfectly well (and correctly) that carp
have no teeth in their mouths...But who knew that fish had teeth in
their throats? Weird.

I've learned more than I ever wanted to know about these fish, today.
For instance, if we ever feel like fishing to catch grass carp, forget
the worms, we should use cherry tomatoes or plugs of sod as bait. And if
you catch one in the state of Indiana, it's illegal to throw it back in;
you must kill it and freeze the carcass for the Dept of Wildlife to
confirm. They're apparently edible but annoying to eat because they
contain a lot of large bones.