Most of what Nero says is a parody of former US president Donald Trump.
When Ralphus (the ancient Romanized version of Ralph, the Warner Bros. watchman) enters Nero's room with the Warners, he says "Duh, Mr. De Niro" - a reference to the actor Robert De Niro.
As the camera pans around the interior of the Smithsonian Museum before Pinky and Brain have materialized, the soundtrack intones three ominous notes on the clarinet. These are the same notes which are heard repeatedly (also on the clarinet) in [Where Is Everybody? (1959)], music by [Bernard Herrmann].
The tribunal announces "General Corbulo has quelled the uprising in Britannia! Brexeunt has been defeated!" This is a reference to Brexit, which (in contradistinction to the quote) England passed and left the European Union.