(at about 7 minutes) When Tim watches Boss Baby exit the car, Tim is wearing a shirt with the digits '01' imprinted. However, when he gets down the stairs, the digits change to '02'. This indicates his being relegated to second place by Boss Baby.
When Boss Baby is showing Tim "Lamb Lamb", and explains that there are newer better toys now, his reference toy is actually Voltron, a 1980s character now owned by DreamWorks.
When Boss Baby and Tim are looking for the plans, Boss Baby throws his disguise into the bin. The way it lands in the bin directly mirrors The Spider-Man story 'Spider-Man no More'. Tobey Maguire, who voices the older Tim portrayed Peter Parker / Spider-Man for three movies, the second of which - Spider-Man 2 (2004) - also pays homage to this iconic image.
When Tim and The Boss Baby move to the back of the bouncy dog and escape it parodies Ace Ventura: When Nature Calls (1995) when Ace squeezes out the back of an animatronic rhino.
Many people were astounded when this was revealed to be a Nominee for the Academy Award for Best Animated Feature. They also expressed alot of anger that it was nominated over the better received The Lego Batman Movie (2017). It even boasts the lowest Tomatometer of the five nominees, sitting at only 52% when compared to 70% for Ferdinand (2017), 83% for Loving Vincent (2017), 93% for The Breadwinner (2017), and 97% for Coco (2017).
When Tim makes fun of the Boss Baby for wearing diapers, he responds with a comment about astronauts and NASCAR drivers wearing diapers. This is referring to the famous story of Lisa Nowak who reportedly wore diapers as she drove from Houston, TX to Orlando, FL continuously.
While Tim describes his parents' exciting jobs in marketing, a shot of them "launching" new products shows them simultaneously turning launch keys in an allusion to the opening sequence of WarGames (1983).
When the babies are caught having a meeting and they resume acting like babies, the music heard is the first few bars of the theme song from The Banana Splits Adventure Hour (1968), a popular kids Saturday morning show in the 1960's, whose main characters (actors in life-sized animal costumes) were inspired by The Monkees (1966).
The 12th DreamWorks Animation film to be nominated for the Academy Award for Best Animated Feature, and the first since How to Train Your Dragon 2 (2014).
Though it proved to be a box office success, grossing nearly $500 million worldwide, it was a critical disappointment. This would be the opposite of DreamWorks Animation's next film, Captain Underpants: The First Epic Movie (2017), which was a critical success, but grossed only $51,506,681 worldwide.
The eighth Dreamworks Animation film to be nominated for the Golden Globe for Best Animated Feature, after Bee Movie (2007), Kung Fu Panda (2008), How to Train Your Dragon (2010), Puss In Boots (2011), Rise of the Guardians (2012), The Croods (2013), and How to Train Your Dragon 2 (2014). Of these, only How to Train Your Dragon 2 has won. Bee Movie lost to Ratatouille (2007), Kung Fu Panda lost to WALL-E (2008), How to Train Your Dragon lost to Toy Story 3 (2010), Puss In Boots lost to The Adventures of Tintin (2011), Rise of the Guardians lost to Brave (2012), and The Croods lost to Frozen (2013). This ended up losing to Coco (2017).
When Tim's father answers the call from Puppy Co. and says that they are on their way, Tim tips back the head of a bust, presses a button, the fireplace slides apart and his parents slide down the two poles. This pays homage to the original Batman TV series, where Batman and Robin slide down the poles to get to the Bat Cave.
The voice of Francis Francis was supposed to be provided by Kevin Spacey. He was replaced by Steve Buschemi. Kevin Spacey plays Francis Underwood, a conniving politician in House of Cards (Netflix, 2013).
In the beginning of the movie, Timothy has just finished being sung to by his parents, and they ask him if he would like a baby brother. If you look at the mom's belly, she is already pregnant.
The Boss Baby, voiced by Alec Baldwin, speaks of writing the best memo of his career. Baldwin's character Jack Ryan in The Hunt for Red October (1990) comments about writing a memo the next time he gets a bright idea.
DreamWorks Animation's 4th biggest opening for a non-sequel, opening to $50.2 million. It's only behind Home (2015) which opened to $52.1 million, Monsters Vs. Aliens (2009) which opened to $59.3 million, and Kung Fu Panda (2008) which opened to $60.2 million.
This isn't the only film that Tobey Maguire is the narrator/adult version of character. He did the same previously for the film Labor Day, where he played the narrator/adult son of Kate Winslet.
The only time Tim's mom is shown pregnant is in the beginning right before his dad asks if he wants a baby brother. Before that she was not shown as pregnant.
The trivia items below may give away important plot points.
Near the beginning, when the toy steam train is being activated, different toys foreshadow the plot. First there is a taxi, in which the baby is delivered; then a police car and fire engine, in which the babies chase Tim; then a barn, referring to the family going to Puppy Co.; then a game of Mouse Trap, in which Tim and Boss Baby get sent to Francis Francis; then an airplane, in which Tim's parents fly; then a pirate ship, referring to Tim and Boss Baby imagining their plane is a pirate ship; then a Habitrail, in which Tim climbs to get to his parents; then a rocket, which is where the Forever Puppies are being launched.
The scene where Tim and the Boss Baby attempt to steal and replace a file from Puppy Co. is a parody of the famous opening scene from Raiders of the Lost Ark (1981) in which Indiana Jones attempts to steal an idol from a temple.
In the scene where Tim discovers the Boss Baby on the phone to Baby Corp, a Light Brite Toy can be seen in the background depicting a graph with "Babies" going down and "Puppies" going up - a hint of the baby's mission.
The trap used to catch Tim and the baby is an oversized and slightly cruder version of the 60s game "Mousetrap", all the way down to the cage that ensnares them.
When Eugene is dressed up as a nanny-type woman to "take care" of the boys, he resembles Mary Poppins. Then Francis Francis says that she's "practically perfect in every way" which is how the titular character of Mary Poppins (1964) is described in her movie.
The bed Timothy's second daughter is in at the end of the movie says her birthdate is March 31st, 2017; the same day the movie was released. This indicates that the main action of the movie is not based in present day. Further evidence that the movie is not set in the present day is the airplane that Timothy's parents take which appears to be a DC-10 that is no longer used for passenger travel.
The tags on the Puppy Co limo say Mar 1978. The tag on the Templeton station wagon is the same color. No cell phones, dial TVs, Tim's cassette tape recorder, parents' cameras, airplanes, everyone dressed up at the airport, cars, the Atari 2600, the high chair, baby crib, and many more items suggest the movie is set in the late 70s, probably 1978.