When Tim is in the garden, he is running to the garden door. He is just an approximate metre away from some cobbles, although when he is stopped by Boss Baby and his crew, he is further away.
Jimbo protects the boss from Tim's vacuum cup arrows and they hit him in the back. But when Tim passes them his whole body is covered by arrows.
When Tim and Boss Baby go into the X-ray luggage scanner at the airport, they are both wearing helmets. When they come out, the helmets are gone and not seen in the scanner.
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.
The milk that Tim spills onto the table by overfilling his glass disappears when the scene cuts back to him.
Despite being toothless, Boss Baby has no speech impediment. There are certain letters that can't be pronounced without teeth.
In the dinner scene, the milk carton impossibly holds enough milk to spill over Tim's equally sized cup.
(at about 6 minutes) Tim's toy train is running on electricity, however it is emitting steam, which is not really produced by a power current.
(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 Voltron toy repeatedly says, "Destroy!" An odd thing to hear from the non-verbal Defender of the Universe.
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.
Tim's dad holds up four digits when he says "three weeks".