Continuity mistake: When Buddy's owner is chasing Josh and Buddy in his truck, there is a scene that shows the truck approaching the water which is a couple of hundred feet away. As the camera cuts back to the driver, he does way too many things before the truck goes in the water (slams on brakes, steering wheels falls off). When about 10 seconds has lapsed, the exact same camera angle is shown of the truck being a couple of hundred feet from the water. The truck would have already been in the water by then.
Continuity mistake: In the scene where Josh is making a doghouse for Buddy out of a cardboard box, he puts a smiley face on it. In the close-up, he draws two long lines for eyes, and a thin smooth curve for a smile. A second later, the eyes are dots and the smile is drawn in a heavy, messy line that's thicker on the left side than the right.