When Tim discovers that Boss Baby can talk, Boss Baby proceeds to analyze Tim's file by picking it up from atop his briefcase. However in the preceding shots, there is no folder on top of his briefcase.
(at about 7 minutes) When Tim watches Boss Baby exit the car, Tim is wearing a top with the digits '01' imprinted. However, when he gets down the stairs, the digits change to '02'. The filmmakers did this to suggest that Tim was number one in his parents' hearts. The number changed the moment Boss Baby walked in the door, suggesting that the baby was the new number one and Tim was second.
The goof item below may give away important plot points.
When Francis E. Francis falls into the vat of baby formula, he comes out as a literal baby. However Francis did mention the reason he was fired from Baby Corp, because he was lactose intolerant to the formula which meant the youth renewal part no longer has an effect on him.