After killing his own henchman Braine tells West to precede him, which he does, but when the scene changes Braine is in front of West despite being in a wheelchair moving a lot slower than West's walking pace.
When Artie rolls the ink onto the typeface it is an ordinary news page with columns of text, a far cry from the detailed poster that results.
One of the world leaders Braine planned to substitute was "Archduke Maximilian of France." France has never had a system of Archdukes. There was a famous Archduke Maximilian of Austria (and Emperor of Mexico), but he was killed by firing squad in 1867 (an event previously used as a backstory in The Night of the Eccentrics (1966)), and this episode takes place in 1872.
One of the world leaders Braine planned to substitute was Prime Minister Luis Bravo of Spain. This would have been impossible since he had not only been out of office since 1868, but dead since September 1, 1871, 10 months before this episode takes place (July 1872).
Artie distracts the guards into looking through a viewer (possibly a stereoscope) at a picture of Lillian Russell. A newspaper shown earlier in the show dates the beginning of this adventure as July 11, 1872 (see Trivia), at which time Lillian Russell was five months shy of her eleventh birthday. Her stage career did not begin until she was eighteen, in 1879. After spending some years in England, her career and fame in the US did not flourish until her return to New York in 1885.
When looking through the window into the phony White House meeting room, West comments that "This must be a one-way mirror." The one-way mirror wasn't patented until 1903.