Continuity mistake: There's an electrical outlet on the wall below the window (aligned with the window shade's loop) in Sid's room near the Megadork poster, but when Sid throws Woody to the floor and raises the shade (before he scorches Woody's forehead with the magnifying glass), that outlet has vanished.
Continuity mistake: All the walls in Andy's room have white wainscoting with the cloud wallpaper on the upper part of the walls, but in the opening shot of the room we see behind the "saloon" box that the cloud wallpaper covers the wall all the way down to the baseboard. The tall dresser isn't where it should be as well. (00:00:40)
Continuity mistake: Near the start, when Andy uses the recliner chair's footrest to catapult Woody to the couch, the footrest remains extended while Andy's with his mother, but a moment later when Andy grabs Woody to head upstairs the recliner footrest has closed on its own. (00:03:10)
Continuity mistake: When Buzz is in Sid's sister's room, Woody comes up to it disguised in the Christmas lights. He then leaves them beside the door before he goes in. When they leave the room, the lights are gone. Later the lights return when Woody goes to get them, but there are fewer of them. (00:47:22)
Continuity mistake: While Buzz sets out to prove he can fly he slides down the loop car track, and in the shot from his POV the world globe is missing from the top of the dresser beside the door.
Continuity mistake: When Rex and Mr. Potato head pop out of the moving box lots of packing foam pops out, yet later when the box spills out in the moving truck there is not any packing foam. (01:09:07)
Continuity mistake: When the army soldiers are yelling into the baby monitor that the kids are heading up to Andy's room, the baby monitor is right in front of Woody on the floor. Yet, when the camera pans out to show all the toys scrambling for their places the monitor is gone, and Hamm is right in front of Woody. Then, when the camera zooms back in to show Woody, the baby monitor has reappeared. (00:12:30)
Continuity mistake: Before Woody uses the remote control to have RC push Buzz off the desk, there are red, yellow, and blue pushpins in an empty area of the bulletin board, but after RC hits the bulletin board, in the closeup of the pushpins falling off those colors have changed to green, red, and yellow, with the green pushpin remaining in the empty space, but when the bulletin board starts to fall over that green pushpin is gone and it's back to the red, yellow, and blue pushpins.
Continuity mistake: In Andy's room, the general ("generil") store box under the crib near the closet door has a cow illustration on its right side, but in the next few shots there's a drawing of two windows on that side of the box, and then it keeps switching between the cow and two windows in following shots.
Continuity mistake: After Sid tapes Buzz to the rocket, when the thunder and lightning occur there's a shot of the window in front of Sid, and the window pane molding with the two handles at the bottom of the lower window is missing. When Sid walks over to that window it's back.
Continuity mistake: In Sid's room, there's a lightbulb hanging over the table (which he turns on when he switches the doll's and pterodactyl's heads), and its electrical cord that hangs beside the lava lamp (filled with toy heads) vanishes and reappears a few times during the scenes there.
Continuity mistake: At the start, when Andy uses the remote control to slam RC (and Woody) into the "bank" box it's pushed under the crib with all of its flaps open, but when Andy takes Molly and leaves the room all of the "bank" box flaps are closed up.
Continuity mistake: After Woody tosses the string lights to Andy's toys at the window Mr. Potato Head hangs onto the end of it, but in the shot from behind Andy's toys when Woody's shaking Buzz's arm and imitating his voice, we see the outside of Sid's window and the string lights have vanished, then they reappear.
Continuity mistake: During the scenes in Andy's room, the light switch plate on the wall near the door vanishes and reappears in some shots.
Continuity mistake: While Andy's falling asleep, when Potato Head and Rex pop out of the Eggman Mover's box it has "Andy's toys" written on one side and the adjacent side is solid - no openings, but when Woody opens this box in the moving truck, there are now open handle cutouts on the two adjacent sides to where "Andy's toys" is written.
Continuity mistake: When Buzz and Woody are attempting to enter the truck towards the end, they ride RC and grab a hold of Slinky to help pull them up. RC loses power and Slinky starts to be pulled onto the road. When he touches the floor to stop him falling he actually pushes against the flow of the road. (01:11:50)
Continuity mistake: When RC hits the notice board in Andy's room, quite a lot of thumb tacks fall off it and land beside Buzz, yet there seems to be the same amount of tacks on the board after the incident as there were before. (00:26:55)
Continuity mistake: Buzz, while pushing the tool box off of the blue basket Woody is in, stretches to about 3 times the length he normally could from that position. When he first starts pushing against the window sill with his feet, he stretches out fully a few seconds later, about half the length of Sid's desk. He continues to push the box over and says "Almost there..." before he does and we can see he still has his feet on the window sill. Most people will have to watch it for a better understanding. (00:59:37)
Continuity mistake: When Andy's mom suggests to Andy they go out to eat at Pizza Planet and that Andy can only bring one toy, Woody picks up the magic 8 ball which was next to him and asks if Andy will pick him. If you see in the earlier shots the ball wasn't there. (00:25:50)
Continuity mistake: When Sid is setting the alarm clock, he sets it for about 8:25, when the alarm goes off the next morning, it's actually at 8:00. (00:55:42)
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