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 hallway of the school, Omri and Patrick are arguing because Patrick is trying to show Little Bear and Boone to some classmates. Patrick is against the wall as Omri yells at him. Note the goof when the young actor playing Patrick mouths much of Omri's dialogue in anticipation of his own lines.
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.
In the end credits, Erik Stabenau is listed in the cast as "Ferengi" (one of the alien races seen on Star Trek: Deep Space Nine). However, the word is incorrectly spelled as "Firengi".