The rat is variously brown and white in different scenes.
When Omri goes to pick up one of the figures from the cupboard, the closeup shows it on the top shelf. In the external shot he picks it up from the bottom of the cupboard.
When Omri is opening his birthday presents around the kitchen table, the rat-in-the-ball is on the table; two seconds later, it's gone, with nobody acting as having picked it up.
When Omri and his mother are looking at the cupboard, Omri closes the door. In the next shot, the door is open.
On the first morning after Omri discovers Little Bear, his mother walks him to school wearing a denim button down shirt and black leggings, but when they get home that day, she is wearing pants and a floral shirt.
In the Darth Vader/T-Rex scene, Erik Stabenau plays a Star Trek alien, credited as "Firengi". The correct spelling is "Ferengi."
When Omri and Patrick are arguing in the school hallway, Patrick mouths much of Omri's dialogue.
The movie appears to follow the time travel rules laid out in the book. The cupboard summons the consciousnesses of real people and animals from the past to be pulled into figurines. This does not explain the enlivenment of Darth Vader, RoboCop, and Star Trek aliens, who are purely imaginary beings. By the established logic, these figurines should come to life as Hollywood actors (or even amateur cosplayers) wearing the costumes of Darth Vader, et al.
A schoolboy names John F. Kennedy as the youngest-ever President of the United States. That honor belongs to Theodore Roosevelt. The matter is often confused because JFK was the youngest-ever *elected* POTUS, while TR succeeded as an emergency President when his benefactor William McKinley died. TR became an elected POTUS three years later.