Continuity mistake: After the cat opens Jack's playpen the toys in front appear/disappear randomly between shots. Also the opening of the door changes when Greg brings the rum.
Continuity mistake: When Jack sees the glue bottle it turns 180° between shots, check the position of the label. One could argue that both sides have a label, but a shot later the kid is grabbing the glue and there's no label on the side facing the camera.
Continuity mistake: When Jack is about to grab the remote control, check the pattern on the carpet: The position of the remote changes.
Continuity mistake: When baby Jack spills the glue, the stain changes its shape drastically between the first and immediate second shot.
Continuity mistake: When Greg tries to calm down the baby after showing him Elmo, the position of Jack's hands on the crib are not continuous between shots.
Continuity mistake: During the football game Bernard's sweat stains on the sweatshirt appear/disappear randomly.
Continuity mistake: When Bernard Focker breaks the toilet and blue liquid spills all over, the baby's hairstyle swaps between the first and second shot.
Continuity mistake: Jack says "we have 23 minutes before they cut the cake". Next shot shows the dog and cat sharing a piece of cake. Next shot shows the cake not cut yet.
Continuity mistake: When Bernie is on the toilet, his feet go from wearing socks to no socks.
Answer: Truth serum doesn't automatically make you speak the absolute truth - all it can do is make you say what you believe to be the truth. If Gaylord believed himself to be Jorge's father, then he would say that under the truth serum, even if it ultimately turned out not to be the case.
Tailkinker ★
Gaylord (Greg) was also drunk when he went on his monologue of spilling "secrets" about others in the room.