Max jumps onto the circus train just as it is going into a tunnel. While he and Snowball are subsequently fighting the wolves in the driver's cabin, you can see through the windows from the lights that the train is still all the time inside the tunnel. Next, when the driver stops the train and immediately everybody gets out, they are in an open landscape.
The scene starting from ~14:00 where Max tries to reach out for the toy ball "busy bee", the ball's location changes in between shots after Duke nudges the sofa table.
At the farm, a red fox sneaks upon Max and ambushes him in a predatory manner. Common foxes are very shy, are not aggressive, and do not eat domestic dogs. Also, common foxes are very athletic, yet physically weaker than domestic dogs.
During scenes in the city, the pink blossoms show crabapple trees are in bloom, so it is clearly springtime. When Max and his family go to the farm, he hears crickets chirping, but crickets don't chirp until the middle of summer.
On the way to the farm, Max and Duke want to stick their head out of the window. The mom pushes the power window down from her side. Most cars do not have controls on the front passenger door for other windows.
Katie and Chuck's SUV has the same license plate (HQO6874) as the circus truck.
Snowball's superhero costume has clear holes for eyes, yet, when Snowball wears it, his eyelids are covered too.
At the farm when they're reading the story of Little Red Riding hood, Liam opens the book from the center which Max refers as "first page" and the story seems to start from quite the beginning, although it is the middle of the book. The book also isn't a compilation of multiple different stories, so this does not make sense.