Continuity mistake: Before the staff meeting, when Woody gets his doodle pad we see the outlet under the crib, but then the outlet vanishes, and reappears later.
Continuity mistake: When Buzz wants to prove that he can fly, he jumps off Andy's bed and ends up on the loop car track, and the three stacked wood blocks (letters A, C, E) suddenly appear in front of the wicker hamper between shots.
Continuity mistake: When Buzz watches the TV commercial and realizes that he's really a toy, by the time "Al's Toy Barn" is mentioned and he reads "made in Taiwan" on his arm, one of the soda cans on the floor changes its position and the trash bin with the crumpled paper around it vanishes.
Continuity mistake: In the scene where toys in Sid's room make their first appearance, they crowd around the middle of the room and pull at Janie's body and the Pterodactyls head. The shot cuts to Woody on Buzz looking horrified. When it goes back to the toys, they're dragging a different dolls body away (the same one that is seen sitting for tea with Buzz in Hannah's room in a later scene). (00:40:50)
Continuity mistake: When Buzz looks at his foot and sees ANDY written on it, at first it's sloppy and a bit backward with a misshapen A, but when the angle changes it's a lot neater. (00:22:05)
Continuity mistake: When Buzz and Woody are riding RC, holding onto Slink in the end, there's a shot where the truck turns to the left on a bend. Slinky gets stretched further, and RC goes off to the right side of the road due to centrifugal force. We can see that RC is going to go under a parked car. The camera switches to the front and we see the car pass from further right. They never end up going under it and tangling Slinky in the wheel. (01:12:00)
Continuity mistake: The objects on Hannah's play table change position between two consecutive shots. Most notably Buzz's arm holding the teapot, as well as Buzz's legs. (00:49:20)
Continuity mistake: When Woody opens the back door on the moving van, the ramp handle is black. But when Rocky Gibraltar uses it, it is red.
Continuity mistake: In the opening scene in Andy's room, Woody's expression is semi-smiling with his mouth closed. Then, when 'You've Got A Friend In Me' plays and Andy takes him out of the room, Woody's expression changes to a blank stare with his mouth semi-open. When Andy returns to his room and places Woody on the bed, his expression is back to the first one with mouth closed. It was not established yet that Woody was 'alive', so his expression shouldn't have been changing at this point.
Continuity mistake: When Buzz and Woody escape the rocket, and fall down, Buzz has tape on the front. But next shot the tape is not there.
Continuity mistake: Near the start, when Woody mentions the party being moved to today, there are 2 black spots on the wheel by the toy box that change place. Note the spoke of the wheel.
Continuity mistake: Towards the end when Potato Head and Ham are playing Battleship and Woody is yelling from Sid's room, Buzz is wearing the apron that Hannah put on him. He's wearing it throughout that whole scene except when the toys in Sid's room are fixing him and Woody says; "you're not gonna eat him, you monsters."
Continuity mistake: When Woody plans to knock Buzz behind a desk, if you look closely at the globe in a box next to the bulletin board, it is slightly off-position in its stand. Later, when the bulletin board begins to fall on the globe, the globe is positioned correctly. (00:24:40 - 00:26:00)
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