Deliberate mistake: When Lilo is told to think of a name for her "dog" while at the Aloha Animal Rescue, there's an adoption document on the desk. The document's paragraph is in fact an acknowledgment of appreciation for this movie's production. Although it's only briefly seen twice, there's sufficient time to read a few words, such as "project Lilo and Stitch" or "at Disney-MGM Studios," and particularly in the close-up as it's being stamped "making of Lilo and Stitch," the last words of the paragraph. (00:27:00 - 00:27:25)
Continuity mistake: When Dr. Doppler and Jim first observe their ship, Dr. Doppler is right next to Jim when he points it out. When the shot changes to a long shot, they're much farther apart. (00:16:55)