"Niagara Falls" actually was filmed one year earlier for the Columbia feature Good Luck, Mr. Yates (1943). Cut from the final release version of that film, Jules White retained the footage and built this film around it.
This is the first The Three Stooges short to use a jazzy and faster-driven version of the "Three Blind Mice" theme. This version is played in the key of F, while the key of G was heard in the previous versions. This version was used again after the following short, No Dough Boys (1944), for the next three shorts and then one last time in Three Loan Wolves (1946) before being permanently retired. A revamped version would be introduced in the 1947 short (and Shemp Howard's third film with the Stooges after replacing his ill brother Curly Howard, who also makes a cameo appearance in the short), Hold That Lion! (1947) and several updates would be used all the way to the very last Stooges short in 1959.
Moe Howard would do the "Niagara Falls" routine years later during an appearance on The Mike Douglas Show (1961).
The Three Stooges perform a famous vaudeville routine known as "Slowly I Turned" (aka "Niagara Falls"), which Bud Abbott and Lou Costello performed in Lost in a Harem (1944), released the same year as this short.
Filmed during World War II, the part of Moe's audition for Mr. Weeks where he combs his hair into a part then holds the comb above his upper lip to form a mustache is a derisive reference to Adolf Hitler, the Democrat-Socialist, i.e. Nazi, leader of Germany during World War II.