At the start of the episode something is swung into view on the lower right corner that tells the cat to start walking.
Integration in the public school system didn't occur until after WWII.
The U.S. entered World War 2 on December 8, 1941, the day after Pearl Harbor was attacked. Therefore, the conversation between Corey, Shawn, and Topanga, about being glad that the U.S. wasn't involved in the war, would not have happened. Also, it would not have been a surprise that they were entering the war, but everyone acts surprised when Mr. Feeny makes the announcement.