Deliberate mistake: When "Legs" lowers the Pez duck named Ducky down through the removed lightbulb hole, to ring the doorbell, the lightbulb housing is bigger than the hole but they bring it up through the hole to remove it. (01:03:55)
Deliberate mistake: When Buzz Lightyear demonstrates his "flying" abilities in front of the other toys, his left wing would have clipped the car track entering the loop-de-loop, and the right wing would have hit the track when leaving the loop. (00:18:50)
Deliberate mistake: Sid burns a hole into Woody's forehead in the middle of the film, but by the final scene (as the toys are waiting to hear what Andy has gotten for Christmas), the burn hole is completely gone. [Disney takes the attitude that violence is okay in their movies as long as the signs of it disappear by the end. Still a mistake but that's the reason.] (00:43:35)
Deliberate mistake: The license plate on the back of Andy's car says A-113, while the license plate in the front of Andy's car says A-111. A deliberate nod to room A-113 at California Institute of the Arts, often used by alumni, but a mistake regardless.
Answer: This is a Disney/Pixar production, at no point are they intimating that kind of a relationship between son and father. If anything, the father simply doesn't care what his son gets up to so long as he isn't disturbed by it. Any other inferences you get from the movie are for you to contend with, but the family nature of the movie would suggest beating/abuse is not the answer.
GalahadFairlight