Continuity mistake: The sequence in which Dragon is chasing Mrs. Brisby through the field, up the tree and eventually into the mill's lake, watch his eyes. The original placement is (from viewer's perspective) blue on the right and gold on the left. When he chases her up the tree the gold one is visible on the right, it then switches back when the camera cuts back to a wide shot. This happens again a few seconds later near the lake.
Continuity mistake: While searching for an entrance in the rose bush, Mrs. Brisby grabs Jeremy by the beak and tells him to be quiet or else. In this scene, Mrs. Brisby's right arm changes position. At first it's wrapped around Jeremy's beak, but then suddenly it appears on top in between shots.
Continuity mistake: While Mrs. Fitzgibbons is in the bedroom talking to her husband about NIMH, she pulls a window shade all the way down. But from the next view, where several rats are transporting an extension cord across the front yard's walkway, the shade is back to its original position again - about halfway up.
Continuity mistake: When Nicodemus is telling Mrs. Brisby that he looked at the words under the latch on the door and understood them, there is a clear, large label under the door. Then a different angle is shown and there is no label on any of the doors, but you should be able to see it still.