The rat changes color from brown to white.
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 Ferengi from Star Trek universe. In the credits, the word is incorrectly spelled as "Firengi".
When Omri and Patrick are arguing at school, Patrick mouths much of Omri's dialogue.
In the scene right before Little Bear and Boone are sent back, Little Bear is sitting in front of a tiny fire, and he hands some fuel to Omri. Omri reaches over the fire for it, and we clearly see his fingers go through the flame. And yet, he doesn't flinch at all. Of course, the fire may be too small to do any damage.
The movie appears to follow the time travel rules laid out in the book. People and animals have their consciousnesses projected across time and 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 perhaps amateur cosplayers) wearing the costumes of Darth Vader, et al.