The mule Algebra was actually a female donkey named Dinah. She was part of the Roach Studio's stable of animals. She appeared in several other shorts such as Hook and Ladder and Free Wheeling.
Every time we see Algebra sitting whenever she hears a bell, it's actually shot in reverse. Mules cannot be taught to sit so they would film the mule raising up from a laying down position and play it backwards.
When Algebra laughs at Barclay's attempts to move her, it's a voice over of former Our Gang member Mickey Daniels.
When Algebra pushes Wally's mother into the fountain on the lawn the mother emerges spewing water like a fountain figure. Algebra let's out with the wild laugh at her, the laugh is that of Mickey Daniels. One of the gang in an earlier day.
Buckwheat is a girl played by Willie Mae Taylor in this short. The character would soon become a boy when Billie Thomas assumed the role.