This was Walt Disney's favorite film made by his studios (source: DVD extras).
This was the first Walt Disney Animated Classic released on videocassette. Its first video release was in 1981 for rental only, and put on sale in the summer of 1982. It was then repackaged in 1985 and 1989 and again in 1994. Then it was first released on DVD in 2001 and again in 2006, and the newest release in 2010. Dumbo has never gone out of print, thus considered the longest Disney animated feature on video to be in print since it came out.
Timothy Mouse is a replacement for the Robin from the original novel. He was used because elephants are supposed to be afraid of mice.
When Jim Crow plucks the "magic" feather off of the youngest crow's tail, the crow's yell is actually a snippet of dialogue from The Reluctant Dragon. The full line is of the dragon saying, "Well, that's splendid!"
When the drunken Timothy is sliding down the staircase-shaped bubble Dumbo has blown, his laugh is actually that of Mickey Mouse. Also, when Timothy coughs on Jim Crow's cigar smoke, that cough is also that of Mickey (it was specifically heard in both Giantland and Two-Gun Mickey).
While trying to comfort Dumbo, Timothy says, "Lots of people with big ears are famous!" According to animation historian John Canemaker on the 2001 DVD release commentary, the line was recognized by audiences of 1941 as a reference to Clark Gable. The line was also featured in the original theatrical trailer.