When Woody is trapped in a milk crate, he hides under a book. The book is TM-31-210 Improvised Munition Handbook. A US Army manual detailing how to make explosives/weapons/traps from ordinary household materials. Gives another look at just how warped Sid is.
The carpet design used in Sid's house is the same design used in the hotel featured in The Shining (1980).
After the "Hey Hamm, I'm Picasso" gag, Mr. Potato Head says to a toy hockey puck, "What are you looking at, you hockey puck?" As an insult comic, Don Rickles (who voices Potato Head) was famous for calling people a "hockey puck" in his routines.
The toolbox in Sid's room is labelled "Binford". That is the name of the tool company on Tim Allen (the voice of Buzz)'s show, Home Improvement .
There are many books behind Woody when he is giving his speech and some of them are Pixar short films such as Red's Dream, Knick Knack, and Tin Toy. The Tin Toy book even has director John Lasseter's last name on it.
The "Hidden Mickey" is the watch clock in Andy's room.
All of the characters eye blink independently, rather than together - a quirk the artists intentionally incorporated.
The number A113 has appeared in every Pixar film (not the shorts). In this film, as well as its sequel, it is the license plate number on Andy's mom's mini-van.
While Buzz is watching the commercial for Buzz Lightyear, the sound made by Buzz's laser is the same as the sound from the original Star Wars TIE fighters.
Originally, Toy Story was going to be about a bear in a toy store. However, the animators decided it would be hard at the time to animate fur for a bear, so they eventually changed the story to what it is now. They kept the bear design, you can see him on the shelf when Woody has his staff meeting. That same bear went through some design changes, and became Lotso from Toy Story 3.
The moving truck's license plate is "MLY1K9" - a reference to Pixar's resident sheepdog, Molly (one canine).