During the driving scene while discussing Cat Stevens, you can see the rear windows of the car alternate between closed, then part open as the camera cuts back and forth between the characters in the front seat and back seat.
Smitty and Clark bury Pluto while Christian watches, but in the cut to a wider shot, Smitty and Christian bury Pluto, and Clark is nowhere to be seen.
Mitch's burn marks change multiple times.
Forty-one minutes in to the movie, you see Mitch turning the music on a car audio Pioneer MIXTRAX model, which you can see has a blue-tooth symbol and a USB plug on it. That definitely was not around in 1991 in which the movie is set.
When Mitch carries Pluto, it's obviously not Pluto.
In the rolling cast credits at the end of the film, the name of the animal actor (Shiloh) and the character being played (Pluto) have accidentally been reversed.
In performing an impromptu eulogy, Mitch thanks Pluto for deciding to protect a boy (Christian) in trouble when he needed it, but it's never made clear that Christian ever told anyone, even his family, what happened in the playground when Pluto showed up.