This short served as the basis for the final sequence of the feature "Blockheads" ten years later.
As he does in "Big Business", Stan calls out "Babe" at one point to get Oliver Hardy's attention. Babe was Hardy's nickname, and since this was a silent, and they hadn't yet achieved their greatest fame, it wasn't re-shot.
This was remade and expanded using the idea of Ollie being sick from the short Be Big resulting in the feature Sons of the Desert.
Leo McCarey is usually credited with being the "Supervisor" or "Supervising Director" for most Hal Roach comedies of this period. We Faw Down is one of the few Laurel and Hardy films he actually directed himself.